title: Exact and Approximate Unitary 2-Designs: Constructions and Applications

abstract:
  We develop the concept of a unitary t-design as a means of expressing
operationally useful subsets of the stochastic properties of the uniform (Haar)
measure on the unitary group U(2^n) on n qubits. In particular, sets of
unitaries forming 2-designs have wide applicability to quantum information
protocols. We devise an O(n)-size in-place circuit construction for an
approximate unitary 2-design. We then show that this can be used to construct
an efficient protocol for experimentally characterizing the fidelity of a
quantum process on n qubits with quantum circuits of size O(n) without
requiring any ancilla qubits, thereby improving upon previous approaches.


title:
Quantum computing with magnetic atoms in optical lattices of reduced
  periodicity

abstract:
  We investigate the feasibility of combining Raman optical lattices with a
quantum computing architecture based on lattice-confined magnetically
interacting neutral atoms. A particular advantage of the standing Raman field
lattices comes from reduced interatomic separations leading to increased
interatomic interactions and improved multi-qubit gate performance.
Specifically, we analyze a $J=3/2$ Zeeman system placed in $% \sigma
_{+}-\sigma_{-}$ Raman fields which exhibit $\lambda /4$ periodicity. We find
that the resulting CNOT gate operations times are in the order of millisecond.
We also investigate motional and magnetic-field induced decoherences specific
to the proposed architecture.


title:
Interpreting concurrence in terms of covariances in a generalized spin
  star system

abstract:
  The quantum dynamics of M pairwise coupled spin 1/2 is analyzed and the time
evolution of the entanglement get established within a prefixed couple of spins
is studied. A conceptual and quantitative link between the concurrence function
and measurable quantities is brought to light providing a physical
interpretation for the concurrence itself as well as a way to measure it. A
generalized spin star system is exactly investigated showing that the
entanglement accompanying its rich dynamics is traceable back to the covariance
of appropriate commuting observables of the two spins.


title:
On large thermal magnetic fluctuations at the surface of metals and the
  Casimir force between real metals at nonzero temperature

abstract:
  This paper has been withdrawn, because relevant publications, related to the
subject of the paper, were overlooked by the author.


title: How to hide a secret direction

abstract:
  We present a procedure to share a secret spatial direction in the absence of
a common reference frame using a multipartite quantum state. The procedure
guarantees that the parties can determine the direction if they perform joint
measurements on the state, but fail to do so if they restrict themselves to
local operations and classical communication (LOCC). We calculate the fidelity
for joint measurements, give bounds on the fidelity achievable by LOCC, and
prove that there is a non-vanishing gap between the two of them, even in the
limit of infinitely many copies. The robustness of the procedure under particle
loss is also studied. As a by-product we find bounds on the probability of
discriminating by LOCC between the invariant subspaces of total angular
momentum N/2 and N/2-1 in a system of N elementary spins.


title: Spiked potentials and quantum toboggans

abstract:
  Even if the motion of a quantum (quasi-)particle proceeds along a
left-right-symmetric (PT-symmetric) curved path in complex plane, the spectrum
of bound states may remain physical, i.e., real and bounded below). We propose
a generalization. Firstly, we show how the topologically less trivial
(tobogganic) contours may be allowed to live on several sheets of a Riemann
surface. Secondly, the specification of a scattering regime is formulated for
such a class of models.


title: An efficient quantum algorithm for colored Jones polynomials

abstract:
  We construct a quantum algorithm to approximate efficiently the colored Jones
polynomial of the plat presentation of any oriented link L at a fixed root of
unity q. Our construction is based on SU(2) Chern-Simons topological quantum
field theory (and associated Wess-Zumino-Witten conformal field theory) and
exploits the q-deformed spin network as computational background.
  As proved in (S. Garnerone, A. Marzuoli, M. Rasetti, quant-ph/0601169), the
colored Jones polynomial can be evaluated in a number of elementary steps,
bounded from above by a linear function of the number of crossings of the link,
and polynomially bounded with respect to the number of link strands. Here we
show that the Kaul unitary representation of colored oriented braids used there
can be efficiently approximated on a standard quantum circuit.


title: Duality for monogamy of entanglement

abstract:
  We establish duality for monogamy of entanglement: whereas monogamy of
entanglement inequalities provide an upper bound for bipartite sharability of
entanglement in a multipartite system, we prove that the same quantity provides
a \emph{lower} bound for distribution of bipartite entanglement in a
multipartite system.
  Our theorem for monogamy of entanglement is used to establish relations
between bipartite entanglement that separate one qubit from the rest vs
separating two qubits from the rest.


title: A First-Principles Method for Open Electronic Systems

abstract:
  We prove that the electron density function of a real physical system can be
uniquely determined by its values on any finite subsystem. This establishes the
existence of a rigorous density-functional theory for any open electronic
system. By introducing a new density functional for dissipative interactions
between the reduced system and its environment, we subsequently develop a
time-dependent density-functional theory which depends in principle only on the
electron density of the reduced system. In the steady-state limit, the
conventional first-principles nonequilibrium Green's function formulation for
the current is recovered. A practical scheme is proposed for the new density
functional: the wide-band limit approximation, which is applied to simulate the
transient current through a model molecular device.


title: Direct, Loss-Tolerant Characterization of Nonclassical Photon Statistics

abstract:
  We experimentally investigate a method of directly characterizing the photon
number distribution of nonclassical light beams that is tolerant to losses and
makes use only of standard binary detectors. This is achieved in a single
measurement by calibrating the detector using some small amount of prior
information about the source. We demonstrate the technique on a freely
propagating heralded two-photon number state created by conditional detection
of a two-mode squeezed state generated by a parametric downconverter.


title:
Relativistic effects in quantum walks: Klein's paradox and
  Zitterbewegung

abstract:
  Quantum walks are not only algorithmic tools for quantum computation but also
not trivial models which describe various physical processes. The paper
compares one-dimensional version of the free particle Dirac equation with
discrete time quantum walk (DTQW). We show that the discretized Dirac equation
when compared with DTQW results in interesting relations. It is also shown that
two relativistic effects associated with the Dirac equation, namely
Zitterbewegung (quivering motion) and Klein's paradox, are present in DTQW,
which can be implemented within non-relativistic quantum mechanics.


title: Quantum Mechanics and the Weak Equivalence Principle

abstract:
  We use the Feynman path integral approach to nonrelativistic quantum
mechanics twofold. First, we derive the lagrangian for a spinless particle
moving in a uniformly but not necessarily constantly accelerated reference
frame; then, applying the strong equivalence principle (SEP) we obtain the
Schroedinger equation for a particle in an inertial frame and in the presence
of a uniform and constant gravity field. Second, using the associated Feynman
propagator, we propagate an initial gaussian wave packet, with the final wave
function and probability density depending on the ratio m/hbar, where m is the
inertial mass of the particle, thus exhibiting the fact that the weak
equivalence principle (WEP) is violated by quantum mechanics. Although due to
rapid oscillations the wave function does not exist in the classical limit, the
probability density is well defined and mass independent when hbar goes to 0,
showing the recovery of the WEP. Finally, at the quantum level, a heavier
particle does not necessarily falls faster than a lighter one; this depends on
the relations between the initial and final common positions and times of the
particles.


title:
Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and
  Pseudo-Hermiticity

abstract:
  Emphasizing the physical constraints on the formulation of a quantum theory
based on the standard measurement axiom and the Schroedinger equation, we
comment on some conceptual issues arising in the formulation of PT-symmetric
quantum mechanics. In particular, we elaborate on the requirements of the
boundedness of the metric operator and the diagonalizability of the
Hamiltonian. We also provide an accessible account of a Krein-space derivation
of the CPT-inner product that was widely known to mathematicians since 1950's.
We show how this derivation is linked with the pseudo-Hermitian formulation of
PT-symmetric quantum mechanics.


title: Comment on "Quantum Dialogue protocol"

abstract:
  In 2004, Ba An Nguyen [Phys. Lett. A 328, 6-10] has presented a Quantum
Dialogue scheme for simultaneously communicating their messages. In this
comment, we show that the quantum dialogue scheme is not secure against the
intercept-and-resend attack and we propose a modified scheme which is secure
against that attack.


title: Coherent states of non-Hermitian quantum systems

abstract:
  We use the Gazeau-Klauder formalism to construct coherent states of
non-Hermitian quantum systems. In particular we use this formalism to construct
coherent state of a PT symmetric system. We also discuss construction of
coherent states following Klauder's minimal prescription.


title: On non-completely positive quantum dynamical maps on spin chains

abstract:
  The new arguments based on Majorana fermions indicating that non-completely
positive maps can describe open quantum evolution are presented.


title: Optimal purification of thermal graph states

abstract:
  In this paper, a purification protocol is presented and its performance is
proven to be optimal when applied to a particular subset of graph states that
are subject to local Z-noise. Such mixed states can be produced by bringing a
system into thermal equilibrium, when it is described by a Hamiltonian which
has a particular graph state as its unique ground state. From this protocol, we
derive the exact value of the critical temperature above which purification is
impossible, as well as the related optimal purification rates. A possible
simulation of graph Hamiltonians is proposed, which requires only bipartite
interactions and local magnetic fields, enabling the tuning of the system
temperature.


title: Entropy of XY Spin Chain and Block Toeplitz Determinants

abstract:
  We consider entanglement in the ground state of the XY spin model on infinite
chain. We use von Neumann entropy of a sub-system as a measure of entanglement.
The entropy of a large block of neighboring spins approaches a constant as the
size of the block increases. We prove rigorously expression for limiting
entropy which was published before. We observe that the entropy reaches minimum
at product states but increases boundlessly at phase transitions.


title: Several natural BQP-Complete problems

abstract:
  A central problem in quantum computing is to identify computational tasks
which can be solved substantially faster on a quantum computer than on any
classical computer. By studying the hardest such tasks, known as BQP-complete
problems, we deepen our understanding of the power and limitations of quantum
computers. We present several BQP-complete problems, including Local
Hamiltonian Eigenvalue Sampling and Phase Estimation Sampling. Different than
the previous known BQP-complete problems (the Quadratically Signed Weight
Enumerator problem [KL01] and the Approximation of Jones Polynomials [FKW02,
FLW02, AJL06]), our problems are of a basic linear algebra nature and are
closely related to the well-known quantum algorithm and quantum complexity
theories.


title: Cantilever cooling with radio frequency circuits

abstract:
  We consider a method to reduce the kinetic energy in a low-order mode of a
miniature cantilever. If the cantilever contributes to the capacitance of a
driven RF circuit, a force on the cantilever exists due to the electric field
energy stored in the capacitance. If this force acts with an appropriate phase
shift relative to the motion of the cantilever, it can oppose the velocity of
the cantilever, leading to cooling. Such cooling may enable reaching the
quantum regime of cantilever motion.


title: Rotationally invariant multipartite states

abstract:
  We construct a class of multipartite states possessing rotational SO(3)
symmetry -- these are states of K spin-j_A particles and K spin-j_B particles.
The construction of symmetric states follows our two recent papers devoted to
unitary and orthogonal multipartite symmetry. We study basic properties of
multipartite SO(3) symmetric states: separability criteria and multi-PPT
conditions.


title:
Quantum interference and evolution of entanglement in a system of
  three-level atoms

abstract:
  We consider a pair of three-level atoms interacting with the vacuum. The
process of disentanglement due to spontaneous emission and the role of quantum
interference between principal transitions in this process, are analysed. We
show that the presence of interference can slow down disentanglement. In the
limit of maximal interference, some part of initial entanglement can survive.


title: On the quantum analogue of Galileo's leaning tower experiment

abstract:
  The quantum analogue of Galileo's leaning tower experiment is revisited using
wave packets evolving under the gravitational potential. We first calculate the
position detection probabilities for particles projected upwards against
gravity around the classical turning point and also around the point of initial
projection, which exhibit mass dependence at both these points. We then compute
the mean arrival time of freely falling particles using the quantum probability
current, which also turns out to be mass dependent. The mass dependence of both
the position detection probabilities and the mean arrival time vanish in the
limit of large mass. Thus, compatibility between the weak equivalence principle
and quantum mechanics is recovered in the macroscopic limit of the latter.


title: Beam splitting and Hong-Ou-Mandel interference for stored light

abstract:
  Storing and release of a quantum light pulse in a medium of atoms in the
tripod configuration are studied. Two complementary sets of control fields are
defined, which lead to independent and complete photon release at two stages.
The system constitutes a new kind of a flexible beam splitter in which the
input and output ports concern photons of the same direction but well separated
in time. A new version of Hong-Ou-Mandel interference is discussed.


title: Separability criteria and bounds for entanglement measures

abstract:
  Employing a recently proposed separability criterion we develop analytical
lower bounds for the concurrence and for the entanglement of formation of
bipartite quantum systems. The separability criterion is based on a
nondecomposable positive map which operates on state spaces with even dimension
N >= 4, and leads to a class of nondecomposable optimal entanglement witnesses.
It is shown that the bounds derived here complement and improve the existing
bounds obtained from the criterion of positive partial transposition and from
the realignment criterion.


title: On the inconsistency of the Bohm-Gadella theory with quantum mechanics

abstract:
  The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum
Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom
asserts that the solutions of the Lippmann-Schwinger equation are functionals
over spaces of Hardy functions. The preparation-registration arrow of time
provides the physical justification for the Hardy axiom. In this paper, it is
shown that the Hardy axiom is incorrect, because the solutions of the
Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also
shown that the derivation of the preparation-registration arrow of time is
flawed. Thus, Hardy functions neither appear when we solve the
Lippmann-Schwinger equation nor they should appear. It is also shown that the
Bohm-Gadella theory does not rest on the same physical principles as quantum
mechanics, and that it does not solve any problem that quantum mechanics cannot
solve. The Bohm-Gadella theory must therefore be abandoned.


title: Quantum control by von Neumann measurements

abstract:
  A general scheme is presented for controlling quantum systems using evolution
driven by non-selective von Neumann measurements, with or without an additional
tailored electromagnetic field. As an example, a 2-level quantum system
controlled by non-selective quantum measurements is considered. The control
goal is to find optimal system observables such that consecutive non-selective
measurement of these observables transforms the system from a given initial
state into a state which maximizes the expected value of a target operator (the
objective). A complete analytical solution is found including explicit
expressions for the optimal measured observables and for the maximal objective
value given any target operator, any initial system density matrix, and any
number of measurements. As an illustration, upper bounds on measurement-induced
population transfer between the ground and the excited states for any number of
measurements are found. The anti-Zeno effect is recovered in the limit of an
infinite number of measurements. In this limit the system becomes completely
controllable. The results establish the degree of control attainable by a
finite number of measurements.


title:
Quantum Information Processing with Delocalized Qubits under Global
  Control

abstract:
  Any technology for quantum information processing (QIP) must embody within it
quantum bits (qubits) and maintain control of their key quantum properties of
superposition and entanglement. Typical QIP schemes envisage an array of
physical systems, such as electrons or nuclei, with each system representing a
given qubit. For adequate control, systems must be distinguishable either by
physical separation or unique frequencies, and their mutual interactions must
be individually manipulable. These difficult requirements exclude many
nanoscale technologies where systems are densely packed and continuously
interacting. Here we demonstrate a new paradigm: restricting ourselves to
global control pulses we permit systems to interact freely and continuously,
with the consequence that qubits can become delocalized over the entire device.
We realize this using NMR studies of three carbon-13 nuclei in alanine,
demonstrating all the key aspects including a quantum mirror, one- and
two-qubit gates, permutation of densely packed qubits and Deutsch algorithms.


title: Universal programmable devices for unambiguous discrimination

abstract:
  We discuss the problem of designing unambiguous programmable discriminators
for any $n$ unknown quantum states in an $m$-dimensional Hilbert space. The
discriminator is a fixed measurement which has two kinds of input registers:
the program registers and the data register. The program registers consist of
the $n$ states, while the data register is prepared among them. The task of the
discriminator is to tell us which state stored in the program registers is
equivalent to that in the data register. First, we give a necessary and
sufficient condition for judging an unambiguous programmable discriminator.
Then, if $m=n$, we present an optimal unambiguous programmable discriminator
for them, in the sense of maximizing the worst-case probability of success.
Finally, we propose a universal unambiguous programmable discriminator for
arbitrary $n$ quantum states. We also show how to use this universal
discriminator to unambiguously discriminate mixed states.


title: Generic Entanglement and Standard Form for N-mode Pure Gaussian States

abstract:
  We investigate the correlation structure of pure N-mode Gaussian resources
which can be experimentally generated by means of squeezers and beam splitters,
whose entanglement properties are generic. We show that those states are
specified (up to local unitaries) by N(N-1)/2 parameters, corresponding to the
two-point correlations between any pair of modes. Our construction yields a
practical scheme to engineer such generic-entangled N-mode pure Gaussian states
by linear optics. We discuss our findings in the framework of Gaussian matrix
product states of harmonic lattices, raising connections with entanglement
frustration and the entropic area law.

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


title:
Preparation of pure and mixed polarization qubits and the direct
  measurement of figures of merit

abstract:
  Non-classical joint measurements can hugely improve the efficiency with which
certain figures of merit of quantum systems are measured. We use such a
measurement to determine a particular figure of merit, the purity, for a
polarization qubit. In the process we highlight some of subtleties involved in
common methods for generating decoherence in quantum optics.


title:
Quantum secret sharing based on modulated high-dimensional time-bin
  entanglement

abstract:
  We propose a new scheme for quantum secret sharing (QSS) that uses a
modulated high-dimensional time-bin entanglement. By modulating the relative
phase randomly by {0,pi}, a sender with the entanglement source can randomly
change the sign of the correlation of the measurement outcomes obtained by two
distant recipients. The two recipients must cooperate if they are to obtain the
sign of the correlation, which is used as a secret key. We show that our scheme
is secure against intercept-and-resend (I-R) and beam splitting attacks by an
outside eavesdropper thanks to the non-orthogonality of high-dimensional
time-bin entangled states. We also show that a cheating attempt based on an I-R
attack by one of the recipients can be detected by changing the dimension of
the time bin entanglement randomly and inserting two "vacant" slots between the
packets. Then, cheating attempts can be detected by monitoring the count rate
in the vacant slots. The proposed scheme has better experimental feasibility
than previously proposed entanglement-based QSS schemes.


title: Solution of the Lindblad Equation in the Kraus Representation

abstract:
  The so-called Lindblad equation, a typical master equation describing the
dissipative quantum dynamics, is shown to be solvable for finite-level systems
in a compact form without resort to writing it down as a set of equations among
matrix elements. The solution is then naturally given in an operator form,
known as the Kraus representation. Following a few simple examples, the general
applicability of the method is clarified.


title: Adiabatic Computation - A Toy Model

abstract:
  We discuss a toy model for adiabatic quantum computation which displays some
phenomenological properties expected in more realistic implementations. This
model has two free parameters: the adiabatic evolution parameter $s$ and the
$\alpha$ parameter which emulates many-variables constrains in the classical
computational problem. The proposed model presents, in the $s-\alpha$ plane, a
line of first order quantum phase transition that ends at a second order point.
The relation between computation complexity and the occurrence of quantum phase
transitions is discussed. We analyze the behavior of the ground and first
excited states near the quantum phase transition, the gap and the entanglement
content of the ground state.


title: Two-level systems: exact solutions and underlying pseudo-supersymmetry

abstract:
  Chains of first-order SUSY transformations for the spin equation are studied
in detail. It is shown that the transformation chains are related with a
olynomial pseudo-supersymmetry of the system. Simple determinant formulas for
the final Hamiltonian of a chain and for solutions of the spin equation are
derived. Applications are intended for a two-level atom in an electromagnetic
field with a possible time-dependence of the field frequency. For a specific
form of this dependence, the time oscillations of the probability to populate
the excited level disappear. Under certain conditions this probability becomes
a function tending monotonously to a constant value which can exceed 1/2.


title: Playing Quantum Physics Jeopardy with zero-energy eigenstates

abstract:
  We describe an example of an exact, quantitative Jeopardy-type quantum
mechanics problem. This problem type is based on the conditions in
one-dimensional quantum systems that allow an energy eigenstate for the
infinite square well to have zero curvature and zero energy when suitable Dirac
delta functions are added. This condition and its solution are not often
discussed in quantum mechanics texts and have interesting pedagogical
consequences.


title: Secrecy extraction from no-signalling correlations

abstract:
  Quantum cryptography shows that one can guarantee the secrecy of correlation
on the sole basis of the laws of physics, that is without limiting the
computational power of the eavesdropper. The usual security proofs suppose that
the authorized partners, Alice and Bob, have a perfect knowledge and control of
their quantum systems and devices; for instance, they must be sure that the
logical bits have been encoded in true qubits, and not in higher-dimensional
systems. In this paper, we present an approach that circumvents this strong
assumption. We define protocols, both for the case of bits and for generic
$d$-dimensional outcomes, in which the security is guaranteed by the very
structure of the Alice-Bob correlations, under the no-signalling condition. The
idea is that, if the correlations cannot be produced by shared randomness, then
Eve has poor knowledge of Alice's and Bob's symbols. The present study assumes,
on the one hand that the eavesdropper Eve performs only individual attacks
(this is a limitation to be removed in further work), on the other hand that
Eve can distribute any correlation compatible with the no-signalling condition
(in this sense her power is greater than what quantum physics allows). Under
these assumptions, we prove that the protocols defined here allow extracting
secrecy from noisy correlations, when these correlations violate a Bell-type
inequality by a sufficiently large amount. The region, in which secrecy
extraction is possible, extends within the region of correlations achievable by
measurements on entangled quantum states.


title: Delta-Function Potential with a Complex Coupling

abstract:
  We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is
real, \delta(x) is the Dirac delta function, and z is an arbitrary complex
coupling constant. For a purely imaginary z, H has a (real) spectral
singularity at E=-z^2/4. For \Re(z)<0, H has an eigenvalue at E=-z^2/4. For the
case that \Re(z)>0, H has a real, positive, continuous spectrum that is free
from spectral singularities. For this latter case, we construct an associated
biorthonormal system and use it to perform a perturbative calculation of a
positive-definite inner product that renders H self-adjoint. This allows us to
address the intriguing question of the nonlocal aspects of the equivalent
Hermitian Hamiltonian for the system. In particular, we compute the energy
expectation values for various Gaussian wave packets to show that the
non-Hermiticity effect diminishes rapidly outside an effective interaction
region.


title:
Adaptive strategies for graph state growth in the presence of monitored
  errors

abstract:
  Graph states (or cluster states) are the entanglement resource that enables
one-way quantum computing. They can be grown by projective measurements on the
component qubits. Such measurements typically carry a significant failure
probability. Moreover, they may generate imperfect entanglement. Here we
describe strategies to adapt growth operations in order to cancel incurred
errors. Nascent states that initially deviate from the ideal graph states
evolve toward the desired high fidelity resource without impractical overheads.
Our analysis extends the diagrammatic language of graph states to include
characteristics such as tilted vertices, weighted edges, and partial fusion,
which arise from experimental imperfections. The strategies we present are
relevant to parity projection schemes such as optical `path erasure' with
distributed matter qubits.


title:
Effective resonant transitions in quantum optical systems: kinematic and
  dynamic resonances

abstract:
  We show that quantum optical systems preserving the total number of
excitations admit a simple classification of possible resonant transitions
(including effective), which can be classified by analizying the free
Hamiltonian and the corresponding integrals of motion. Quantum systems not
preserving the total number of excitations do not admit such a simple
classification, so that an explicit form of the effective Hamiltonian is needed
to specify the allowed resonances. The structure of the resonant transitions
essentially depends on the algebraic propereties of interacting subsystems.


title: Joint multipartite photon statistics by on/off detection

abstract:
  We demonstrate a method to reconstruct the joint photon statistics of two or
more modes of radiation using on/off photodetection performed at different
quantum efficiencies. The two-mode case is discussed in details and
experimental results are presented for the bipartite states obtained after a
beam-splitter fed by a single photon state or a thermal state.


title: Almost uniform sampling via quantum walks

abstract:
  Many classical randomized algorithms (e.g., approximation algorithms for
#P-complete problems) utilize the following random walk algorithm for {\em
almost uniform sampling} from a state space $S$ of cardinality $N$: run a
symmetric ergodic Markov chain $P$ on $S$ for long enough to obtain a random
state from within $\epsilon$ total variation distance of the uniform
distribution over $S$. The running time of this algorithm, the so-called {\em
mixing time} of $P$, is $O(\delta^{-1} (\log N + \log \epsilon^{-1}))$, where
$\delta$ is the spectral gap of $P$.
  We present a natural quantum version of this algorithm based on repeated
measurements of the {\em quantum walk} $U_t = e^{-iPt}$. We show that it
samples almost uniformly from $S$ with logarithmic dependence on
$\epsilon^{-1}$ just as the classical walk $P$ does; previously, no such
quantum walk algorithm was known. We then outline a framework for analyzing its
running time and formulate two plausible conjectures which together would imply
that it runs in time $O(\delta^{-1/2} \log N \log \epsilon^{-1})$ when $P$ is
the standard transition matrix of a constant-degree graph. We prove each
conjecture for a subclass of Cayley graphs.


title:
Effective Hamiltonian approach to adiabatic approximation in open
  systems

abstract:
  The adiabatic approximation in open systems is formulated through the
effective Hamiltonian approach. By introducing an ancilla, we embed the open
system dynamics into a non-Hermitian quantum dynamics of a composite system,
the adiabatic evolution of the open system is then defined as the adiabatic
dynamics of the composite system. Validity and invalidity conditions for this
approximation are established and discussed. A High-order adiabatic
approximation for open systems is introduced. As an example, the adiabatic
condition for an open spin-$\frac 1 2$ particle in time-dependent magnetic
fields is analyzed.


title:
Coherent single-photon generation and trapping with imperfect cavity QED
  systems

abstract:
  We study analytically the dynamics of cavity QED nodes in a practical quantum
network. Given a single 3-level $\Lambda$-type atom or quantum dot coupled to a
micro-cavity, we derive several necessary and sufficient criteria for the
coherent trapping and generation of a single photon pulse with a given waveform
to be realizable. We prove that these processes can be performed with practical
hardware -- such as cavity QED systems which are operating deep in the weak
coupling regime -- given a set of restrictions on the single-photon pulse
envelope. We systematically study the effects of spontaneous emission and
spurious cavity decay on the transfer efficiency, including the case where more
than one excited state participates in the dynamics. This work should open the
way to very efficient optimizations of the operation of quantum networks.


title:
Localization and its consequences for quantum walk algorithms and
  quantum communication

abstract:
  The exponential speed-up of quantum walks on certain graphs, relative to
classical particles diffusing on the same graph, is a striking observation. It
has suggested the possibility of new fast quantum algorithms. We point out here
that quantum mechanics can also lead, through the phenomenon of localization,
to exponential suppression of motion on these graphs (even in the absence of
decoherence). In fact, for physical embodiments of graphs, this will be the
generic behaviour. It also has implications for proposals for using spin
networks, including spin chains, as quantum communication channels.


title:
No-Cloning and No-Deleting theorems through the existence of
  Incomparable states under LOCC

abstract:
  No-Cloning and No-Deleting theorems are verified with the constraint on local
state transformations via the existence of incomparable states. Assuming the
existence of exact cloning or deleting operation defined on a minimum number of
two arbitrary states, an incomparable pair of states of the joint system
between two parties can be made to compare under deterministic LOCC. We have
restricted our proof with the assumption that the machine states of the cloning
or deleting operations do not keep any information about the input states. We
use the same setting to establish the no-cloning and no-deleting theorems via
incomparability that supports the reciprocity of the two operations in their
operational senses. The work associates the impossibility of operations with
the evolution of an entangled system by LOCC.


title: Quantum Entanglement in the S=1/2 Spin Ladder with Ring Exchange

abstract:
  In this paper we study the concurrence and the block-block entanglement in
the $S=1/2$ spin ladder with four-spin ring exchange by the exact
diagonalization method of finite cluster of spins. The relationship between the
global phase diagram and the ground-state entanglement is investigated. It is
shown that the block-block entanglement of different block size and geometry
manifests richer information of the system. We find that the extremal point of
the two-site block-block entanglement on the rung locates a transition point
exactly due to SU(4) symmetry at this point. The scaling behavior of the
block-block entanglement is discussed. Our results suggest that the block-block
entanglement can be used as a convenient marker of quantum phase transition in
some complex spin systems.


title: Backward Evolving Quantum States

abstract:
  The basic concept of the two-state vector formalism, which is the time
symmetric approach to quantum mechanics, is the backward evolving quantum
state. However, due to the time asymmetry of the memory's arrow of time, the
possible ways to manipulate a backward evolving quantum state differ from those
for a standard, forward evolving quantum state. The similarities and the
differences between forward and backward evolving quantum states regarding the
no-cloning theorem, nonlocal measurements, and teleportation are discussed. The
results are relevant not only in the framework of the two-state vector
formalism, but also in the framework of retrodictive quantum theory.


title: Zeno logic gates using micro-cavities

abstract:
  The linear optics approach to quantum computing has several potential
advantages but the logic operations are probabilistic. Here we review the use
of the quantum Zeno effect to suppress the intrinsic failure events in these
kinds of devices, which would produce deterministic logic operations without
the need for ancilla photons or high-efficiency detectors. The potential
advantages of implementing Zeno gates using micro-cavities and
electromagnetically-induced transparency are discussed.


title:
Quantum study of information delay in electromagetically induced
  transparency

abstract:
  Using electromagnetically induced transparency (EIT), it is possible to delay
and store light in atomic ensembles. Theoretical modelling and recent
experiments have suggested that the EIT storage mechanism can be used as a
memory for quantum information. We present experiments that quantify the noise
performance of an EIT system for conjugate amplitude and phase quadratures. It
is shown that our EIT system adds excess noise to the delayed light that has
not hitherto been predicted by published theoretical modelling. In analogy with
other continuous-variable quantum information systems, the performance of our
EIT system is characterised in terms of conditional variance and signal
transfer.


title:
On the structure of entanglement witnesses and new class of positive
  indecomposable maps

abstract:
  We construct a new class of positive indecomposable maps in the algebra of 'd
x d' complex matrices. Each map is uniquely characterized by a cyclic
bistochastic matrix. This class generalizes a Choi map for d=3. It provides a
new reach family of indecomposable entanglement witnesses which define
important tool for investigating quantum entanglement.


title: Examples of Gaussian cluster computation

abstract:
  We give simple examples that illustrate the principles of one-way quantum
computation using Gaussian continuous-variable cluster states. In these
examples, we only consider single-mode evolutions, realizable via linear
clusters. In particular, we focus on Gaussian single-mode transformations
performed through the cluster state. Our examples highlight the differences
between cluster-based schemes and protocols in which special quantum states are
prepared off-line and then used as a resource for the on-line computation.


title: Local asymptotic normality in quantum statistics

abstract:
  The theory of local asymptotic normality for quantum statistical experiments
is developed in the spirit of the classical result from mathematical statistics
due to Le Cam. Roughly speaking, local asymptotic normality means that the
family varphi_{\theta_{0}+ u/\sqrt{n}}^{n} consisting of joint states of n
identically prepared quantum systems approaches in a statistical sense a family
of Gaussian state phi_{u} of an algebra of canonical commutation relations. The
convergence holds for all "local parameters" u\in R^{m} such that
theta=theta_{0}+ u/sqrt{n} parametrizes a neighborhood of a fixed point
theta_{0}\in Theta\subset R^{m}.
  In order to prove the result we define weak and strong convergence of quantum
statistical experiments which extend to the asymptotic framework the notion of
quantum sufficiency introduces by Petz. Along the way we introduce the concept
of canonical state of a statistical experiment, and investigate the relation
between the two notions of convergence. For reader's convenience and
completeness we review the relevant results of the classical as well as the
quantum theory.


title:
An "anti-Gleason" phenomenon and simultaneous measurements in classical
  mechanics

abstract:
  We report on an "anti-Gleason" phenomenon in classical mechanics: in contrast
with the quantum case, the algebra of classical observables can carry a
non-linear quasi-state, a monotone functional which is linear on all subspaces
generated by Poisson-commutative functions. We present an example of such a
quasi-state in the case when the phase space is the 2-sphere. This example lies
in the intersection of two seemingly remote mathematical theories - symplectic
topology and the theory of topological quasi-states. We use this quasi-state to
estimate the error of the simultaneous measurement of non-commuting
Hamiltonians.


title:
Polynomial invariants and Bell inequalities as entanglement measure of
  4-qubit states

abstract:
  We compare the polynomial invariants for four qubits introduced by Luque and
Thibon, PRA {\bf 67}, 042303 (2003), with optimized Bell inequalities and a
combination of two qubit concurrences. It is shown for various parameter
dependent states from different SLOCC classes that it is possible to measure a
genuine 4-qubit entanglement with these polynomials.


title: Thermalization through unitary evolution of pure states

abstract:
  The unitary time evolution of a critical quantum spin chain with an impurity
is calculated, and the entanglement evolution is shown. Moreover, we show that
the reduced density matrix of a part of the chain evolves such that the
fidelity of its spectrum is very high with respect to a state in thermal
equilibrium. Hence, a thermal state occurs through unitary time evolution in a
simple spin chain with impurity.


title:
Concatenated beam splitters, optical feed-forward and the nonlinear sign
  gate

abstract:
  We consider a nonlinear sign gate implemented using a sequence of two beam
splitters, and consider the use of further sequences of beam splitters to
implement feed-forward so as to correct an error resulting from the first beam
splitter. We obtain similar results to Scheel et al. [Scheel et al., Phys. Rev.
A 73, 034301 (2006)], in that we also find that our feed-forward procedure is
only able to produce a very minor improvement in the success probability of the
original gate.


title: What is paradoxical about the "Three-box paradox"?

abstract:
  This paper is a comment on quant-ph/0606067 by Ravon and Vaidman, in which
they defend the position that the ``three-box paradox'' is indeed paradoxical.


title: Quantum Games in Open Systems using Biophysic Hamiltonians

abstract:
  We analyze the necessary physical conditions to model an open quantum system
as a quantum game. By applying the formalism of Quantum Operations on a
particular system, we use Kraus operators as quantum strategies. The physical
interpretation is a conflict among different configurations of the environment.
The resolution of the conflict displays regimes of minimum loss of information.


title:
Single qubit gates by selective excitation with Jump and Return
  sequences

abstract:
  We discuss the implementation of frequency selective rotations using
sequences of hard pulses and delays. These rotations are suitable for
implementing single qubit gates in Nuclear Magnetic Resonance (NMR) quantum
computers, but can also be used in other related implementations of quantum
computing. We also derive methods for implementing hard pulses in the presence
of moderate off-resonance effects, and describe a simple procedure for
implementing a hard 180 degree rotation in a two spin system. Finally we show
how these two approaches can be combined to produce more accurate frequency
selective rotations.


title:
Sub Shot-Noise interferometric phase sensitivity with Beryllium ions
  Schroedinger Cat States

abstract:
  Interferometry with NOON quantum states can provide unbiased phase estimation
with a sensitivity scaling as $\Delta \theta \sim 1/N_T$ given a prior
knowledge that the true phase shift $\theta$ lies in the interval $-\pi \leq
\theta \leq \pi$. The protocol requires a total of $N_T = 2^{p}-1$ particles
(unequally) distributed among $p$ independent measurements and overcomes basic
difficulties present in previously proposed approaches. We demonstrate the
possibility to obtain a phase sensitivity beating the classical shot-noise
limit using published probabilities retrieved experimentally for the creation
of Schr\"odinger cat quantum states containing up to N=6 beryllium ions.


title: Quantum decoherence of the damped harmonic oscillator

abstract:
  In the framework of the Lindblad theory for open quantum systems, we
determine the degree of quantum decoherence of a harmonic oscillator
interacting with a thermal bath. It is found that the system manifests a
quantum decoherence which is more and more significant in time. We also
calculate the decoherence time and show that it has the same scale as the time
after which thermal fluctuations become comparable with quantum fluctuations.


title: Perspectives: Quantum Mechanics on Phase Space

abstract:
  The basic ideas in the theory of quantum mechanics on phase space are
illustrated through an introduction of generalities, which seem to underlie
most if not all such formulations and follow with examples taken primarily from
kinematical particle model descriptions exhibiting either Galileian or
Lorentzian symmetry. The structures of fundamental importance are the relevant
(Lie) groups of symmetries and their homogeneous (and associated) spaces that,
in the situations of interest, also possess Hamiltonian structures. Comments
are made on the relation between the theory outlined and a recent paper by
Carmeli, Cassinelli, Toigo, and Vacchini.


title:
Exact analytical solution to the relativistic Klein-Gordon equation with
  non-central equal scalar and vector potentials

abstract:
  We present an alternative and simple method for the exact solution of the
Klein-Gordon equation in the presence of the non-central equal scalar and
vector potentials by using Nikiforov-Uvarov (NU) method. The exact bound state
energy eigenvalues and corresponding eigenfunctions are obtained for a particle
bound in a potential of $V(r,\theta) = \frac{\alpha}{r} + \frac{\beta}{r^2\sin
^2\theta} + \gamma \frac{\cos \theta}{r^2\sin ^2\theta}$ type.


title:
The mother of all protocols: Restructuring quantum information's family
  tree

abstract:
  We give a simple, direct proof of the "mother" protocol of quantum
information theory. In this new formulation, it is easy to see that the mother,
or rather her generalization to the fully quantum Slepian-Wolf protocol,
simultaneously accomplishes two goals: quantum communication-assisted
entanglement distillation, and state transfer from the sender to the receiver.
As a result, in addition to her other "children," the mother protocol generates
the state merging primitive of Horodecki, Oppenheim and Winter, a fully quantum
reverse Shannon theorem, and a new class of distributed compression protocols
for correlated quantum sources which are optimal for sources described by
separable density operators. Moreover, the mother protocol described here is
easily transformed into the so-called "father" protocol whose children provide
the quantum capacity and the entanglement-assisted capacity of a quantum
channel, demonstrating that the division of single-sender/single-receiver
protocols into two families was unnecessary: all protocols in the family are
children of the mother.


title: Scalable Error Correction in Distributed Ion Trap Computers

abstract:
  A major challenge for quantum computation in ion trap systems is scalable
integration of error correction and fault tolerance. We analyze a distributed
architecture with rapid high fidelity local control within nodes and entangled
links between nodes alleviating long-distance transport. We demonstrate
fault-tolerant operator measurements which are used for error correction and
non-local gates. This scheme is readily applied to linear ion traps which
cannot be scaled up beyond a few ions per individual trap but which have access
to a probabilistic entanglement mechanism. A proof-of-concept system is
presented which is within the reach of current experiment.


title: Multipartite Nonlocality without Entanglement in Many Dimensions

abstract:
  We present a generic method to construct a product basis exhibiting
Nonlocality Without Entanglement with $n$ parties each holding a system of
dimension at least $n-1$. This basis is generated via a quantum circuit made of
control-Discrete Fourier Transform gates acting on the computational basis. The
simplicity of our quantum circuit allows for an intuitive understanding of this
new type of nonlocality. We also show how this circuit can be used to construct
Unextendible Product Bases and their associated Bound Entangled States. To our
knowledge, this is the first method which, given a general Hilbert space
$\bigotimes_{i=1}^n {\cal H}_{d_i}$ with $d_i\le n-1$, makes it possible to
construct (i) a basis exhibiting Nonlocality Without Entanglement, (ii) an
Unextendible Product Basis, and (iii) a Bound Entangled state.


title: An Introduction to Quantum Entanglement: a Geometric Approach

abstract:
  We present a concise introduction to quantum entanglement. Concentrating on
bipartite systems we review the separability criteria and measures of
entanglement. We focus our attention on geometry of the sets of separable and
maximally entangled states. We treat in detail the two-qubit system and
emphasise in what respect this case is a special one.


title:
Estimating diagonal entries of powers of sparse symmetric matrices is
  BQP-complete

abstract:
  Let A be a real symmetric matrix of size N such that the number of the
non-zero entries in each row is polylogarithmic in N and the positions and the
values of these entries are specified by an efficiently computable function. We
consider the problem of estimating an arbitrary diagonal entry (A^m)_jj of the
matrix A^m up to an error of \epsilon b^m, where b is an a priori given upper
bound on the norm of A, m and \epsilon are polylogarithmic and inverse
polylogarithmic in N, respectively.
  We show that this problem is BQP-complete. It can be solved efficiently on a
quantum computer by repeatedly applying measurements of A to the jth basis
vector and raising the outcome to the mth power. Conversely, every quantum
circuit that solves a problem in BQP can be encoded into a sparse matrix such
that some basis vector |j> corresponding to the input induces two different
spectral measures depending on whether the input is accepted or not. These
measures can be distinguished by estimating the mth statistical moment for some
appropriately chosen m, i.e., by the jth diagonal entry of A^m. The problem is
still in BQP when generalized to off-diagonal entries and it remains BQP-hard
if A has only -1, 0, and 1 as entries.


title:
The Conventionality of Synchronization and the Causal Structure of
  Quantum Mechanics

abstract:
  Measuring velocities requires the synchronization of spatially-separated
clocks. Because this synchronization must precede the determination of
velocities, no system of clock synchronization--such as that based on
Einstein's presumption of light-speed isotropy--can ever be founded on an
experimentally-validated velocity. I argue that this very old observation,
which lingers in the philosophical literature under the heading
``Conventionality of Synchronization,'' suggests an explanation of why
``spooky'' quantum correlations can transfer no information at any speed,
superluminal or otherwise. This work constitutes the first application of the
Conventionality doctrine outside of Relativity itself.


title: On the non-existence of a universal Hadamard gate

abstract:
  We establish the non-existence of a universal Hadamard gate for arbitrary
unknown qubits, by considering two different principles; namely,
no-superluminal signalling and non-increase of entanglement under LOCC. It is
also shown that these principles are not violated if and only if the qubit
states are of a special form obtained in our recent work [ IJQI (in press),
quant-ph/0505068 ].


title:
Two-atom van der Waals interaction between polarizable/magnetizable
  atoms near magneto-electric bodies

abstract:
  The van der Waals potential of two atoms in the presence of an arbitrary
arrangement of dispersing and absorbing magnetodielectric bodies is studied.
Starting from a polarizable atom placed within a given geometry, its
interaction with a second polarizable/magnetizable atom is deduced from its
Casimir-Polder interaction with a weakly polarizable/magnetizable test body.
The general expressions for the van der Waals potential hence obtained are
illustrated by considering first the case of two atoms in free space, with
special emphasis on the interaction between (i) two polarizable atoms and (ii)
a polarizable and a magnetizable atom. Furthermore, the influence of
magnetodielectric bodies on the van der Waals interaction is studied in detail
for the example of two atoms placed near a perfectly reflecting plate or a
magnetodielectric half space, respectively.


title: Collective Two-Atom Effects and Trapping States in the Micromaser

abstract:
  We investigate signals of trapping states in the micromaser system in terms
of the average number of cavity photons as well as a suitably defined
correlation length of atoms leaving the cavity. In the description of
collective two-atom effects we allow the mean number of pump atoms inside the
cavity during the characteristic atomic cavity transit time to be as large as
of order one. The master equation we consider, which describes the micromaser
including collective two-atom effects, still exhibits trapping states for even
for a mean number of atoms inside the cavity close to one. We, however, argue
more importantly that the trapping states are more pronounced in terms of the
correlation length as compared to the average number of cavity photons, i.e. we
suggest that trapping states can be more clearly revealed experimentally in
terms of the atom correlation length. For axion detection in the micromaser
this observable may therefore be an essential ingredient.


title:
Experimental Observation of Four-Photon Entangled Dicke State with High
  Fidelity

abstract:
  We present the experimental observation of the symmetric four-photon
entangled Dicke state with two excitations $|D_{4}^{(2)}>$. A simple
experimental set-up allowed quantum state tomography yielding a fidelity as
high as $0.844 \pm 0.008$. We study the entanglement persistency of the state
using novel witness operators and focus on the demonstration of a remarkable
property: depending on the orientation of a measurement on one photon, the
remaining three photons are projected into both inequivalent classes of genuine
tripartite entanglement, the GHZ and W class. Furthermore, we discuss possible
applications of $|D_{4}^{(2)}>$ in quantum communication.


title: Casimir edge effects

abstract:
  We compute Casimir forces in open geometries with edges, involving parallel
as well as perpendicular semi-infinite plates. We focus on Casimir
configurations which are governed by a unique dimensional scaling law with a
universal coefficient. With the aid of worldline numerics, we determine this
coefficient for various geometries for the case of scalar-field fluctuations
with Dirichlet boundary conditions. Our results facilitate an estimate of the
systematic error induced by the edges of finite plates, for instance, in a
standard parallel-plate experiment. The Casimir edge effects for this case can
be reformulated as an increase of the effective area of the configuration.


title: Quantum secure direct communication with pure entangled states

abstract:
  We present a quantum secure direct communication protocol where the channels
are not maximally entangled states. The communication parties utilize decoy
photons to check eavesdropping. After ensuring the security of the quantum
channel, the sender encodes the secret message and transmits it to the receiver
by using Controlled-NOT operation and von Neumann measurement. The protocol is
simple and realizable with present technology. We also show the protocol is
secure for noisy quantum channel.


title:
Transport dynamics of single ions in segmented microstructured Paul trap
  arrays

abstract:
  It was recently proposed to use small groups of trapped ions as qubit
carriers in miniaturized electrode arrays that comprise a large number of
individual trapping zones, between which ions could be moved. This approach
might be scalable for quantum information processing with a large numbers of
qubits. Processing of quantum information is achieved by transporting ions to
and from separate memory and qubit manipulation zones in between quantum logic
operations. The transport of ion groups in this scheme plays a major role and
requires precise experimental control and fast transport. In this paper we
introduce a theoretical framework to study ion transport in external potentials
that might be created by typical miniaturized Paul trap electrode arrays. In
particular we discuss the relationship between classical and quantum
descriptions of the transport and study the energy transfer to the oscillatory
motion during near-adiabatic transport. Based on our findings we suggest a
numerical method to find electrode potentials as a function of time to optimize
the local potential an ion experiences during transport. We demonstrate this
method for one specific electrode geometry that should closely represent the
situation encountered in realistic trap arrays.


title: Local extraction of EPR entanglement from classical systems

abstract:
  Coherent states with large amplitudes are traditionally thought of as the
best quantum mechanical approximation of classical behavior. Here we argue
that, far from being classical, coherent state are in fact highly entangled. We
demonstrate this by showing that a general system of indistinguishable bosons
in a coherent state can be used to entangle, by local interactions, two
spatially separated and distinguishable non-interacting quantum systems.
Entanglement can also be extracted in the same way from number states or any
other nontrivial superpositions of them.


title: Non-Hermitian degeneracy of two unbound states

abstract:
  We solved numerically the implicit, trascendental equation that defines the
eigenenergy surface of a degenerating isolated doublet of unbound states in the
simple but illustrative case of the scattering of a beam of particles by a
double barrier potential. Unfolding the degeneracy point with the help of a
contact equivalent approximant, crossings and anticrossings of energies and
widths, as well as the changes of identity of the poles of the S-matrix are
explained in terms of sections of the eigenenergy surfaces.


title: Analysis of entropy of XY Spin Chain

abstract:
  Entanglement in the ground state of the XY model on the infinite chain can be
measured by the von Neumann entropy of a block of neighboring spins. We study a
double scaling limit: the size of the block is much larger then 1 but much
smaller then the length of the whole chain. In this limit, the entropy of the
block approaches a constant. The limiting entropy is a function of the
anisotropy and of the magnetic field. The entropy reaches minima at product
states and increases boundlessly at phase transitions.


title:
Investigation of continuous-time quantum walk by using Krylov
  subspace-Lanczos algorithm

abstract:
  In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on
graphs possessing quantum decomposition (QD graphs) have been calculated by a
new method based on spectral distribution associated to their adjacency matrix.
Here in this paper, it is shown that the continuous-time quantum walk on any
arbitrary graph can be investigated by spectral distribution method, simply by
using Krylov subspace-Lanczos algorithm to generate orthonormal bases of
Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new
type of graphs possessing generalized quantum decomposition have been
introduced, where this is achieved simply by relaxing some of the constrains
imposed on QD graphs and it is shown that both in QD and GQD graphs, the unit
vectors of strata are identical with the orthonormal basis produced by Lanczos
algorithm. Moreover, it is shown that probability amplitude of observing walk
at a given vertex is proportional to its coefficient in the corresponding unit
vector of its stratum, and it can be written in terms of the amplitude of its
stratum. Finally the capability of Lanczos-based algorithm for evaluation of
walk on arbitrary graphs (GQD or non-QD types), has been tested by calculating
the probability amplitudes of quantum walk on some interesting finite
(infinite) graph of GQD type and finite (infinite) path graph of non-GQD type,
where the asymptotic behavior of the probability amplitudes at infinite limit
of number of vertices, are in agreement with those of central limit theorem of
Ref.\cite{nko}.


title: False qubits?: Polarization of light and Josephson junction

abstract:
  We compare two physical systems: polarization degrees of freedom of a
macroscopic light beam and the Josephson junction (JJ) in the "charge qubit
regime". The first system obviously cannot carry genuine quantum information
and we show that the maximal entanglement which could be encoded into
polarization of two light beams scales like 1/(photon number). Two theories of
JJ, one leading to the picture of "JJ-qubit" and the other based on the
mean-field approach are discussed. The later, which seems to be more
appropriate, implies that the JJ system is, essentially, mathematically
equivalent to the polarization of a light beam with the number of photons
replaced by the number of Cooper pairs. The existing experiments consistent
with the "JJ-qubit" picture and the theoretical arguments supporting, on the
contrary, the classical model are briefly discussed. The Franck-Hertz-type
experiment is suggested as an ultimate test of the JJ nature.


title:
Generation and Manipulation of Multi-Color Stationary Light Field Using
  Electromagnetically Induced Transperancy

abstract:
  Dynamic control of a weak quantum probe light pulse for the generation and
quantum manipulations of a stationary multi-color (MC-) light field in a
resonant coherent atomic medium using electromagnetically induced transparency
is proposed. The manipulations have been analyzed based on the analytical
solution of the adiabatic limit in the evolution of MC-light fields resulting
from interaction of the slow probe light with the new fields generated in the
nondegenerate multi-wave mixing scheme. We have found a critical stopping
condition for the MC-light fields where the group velocity of light should
reduce down to zero. Semiclassical dynamics and behavior of specific quantum
correlations of the MC-light fields have been studied in detail for particular
initial quantum states of the probe pulse. The stationary MC-field dynamics are
treated in terms of dark MC-polariton states constructed for the studied
multi-wave mixing processes. We have found the conditions for optimal
manipulation of the MC-light while preserving the delicate quantum correlations
of the initial probe light pulse. The quantum manipulations leading to the
frequency and direction switching of the initial probe light pulse as well as
to the quantum swapping of probe light into the new multi-frequency light
fields have been proposed. The possibilities of the interaction time
lengthening and enhancement of the electric field amplitudes of the stationary
MC-light are also discussed for enhancement of the interactions with weak
quantum fields in the spatially limited media.


title:
Entropic uncertainty relations and locking: tight bounds for mutually
  unbiased bases

abstract:
  We prove tight entropic uncertainty relations for a large number of mutually
unbiased measurements. In particular, we show that a bound derived from the
result by Maassen and Uffink for 2 such measurements can in fact be tight for
up to sqrt{d} measurements in mutually unbiased bases. We then show that using
more mutually unbiased bases does not always lead to a better locking effect.
We prove that the optimal bound for the accessible information using up to
sqrt{d} specific mutually unbiased bases is log d/2, which is the same as can
be achieved by using only two bases. Our result indicates that merely using
mutually unbiased bases is not sufficient to achieve a strong locking effect,
and we need to look for additional properties.


title: Quantum wave equations and non-radiating electromagnetic sources

abstract:
  A connection between classical non-radiating sources and free-particle wave
equations in quantum mechanics is rigorously made. It is proven that
free-particle wave equations for all spins have currents which can be defined
which are non-radiating electromagnetic sources. It is also proven that the
advanced and retarded fields are exactly equal for these sources. Implications
of these results are discussed.


title: Stochastic Schroedinger equation from optimal observable evolution

abstract:
  In this article, we consider a set of trial wave-functions denoted by $| Q
\right>$ and an associated set of operators $A_\alpha$ which generate
transformations connecting those trial states. Using variational principles, we
show that we can always obtain a quantum Monte-Carlo method where the quantum
evolution of a system is replaced by jumps between density matrices of the form
$D = |Q_a> <Q_b|$, and where the average evolutions of the moments of
$A_\alpha$ up to a given order $k$, i.e. $< A_{\alpha_1} >$, $< A_{\alpha_1}
A_{\alpha_2} >$,..., $< A_{\alpha_1} ... A_{\alpha_k} >$, are constrained to
follow the exact Ehrenfest evolution at each time step along each stochastic
trajectory. Then, a set of more and more elaborated stochastic approximations
of a quantum problem is obtained which approach the exact solution when more
and more constraints are imposed, i.e. when $k$ increases. The Monte-Carlo
process might even become exact if the Hamiltonian $H$ applied on the trial
state can be written as a polynomial of $A_\alpha$. The formalism makes a
natural connection between quantum jumps in Hilbert space and phase-space
dynamics. We show that the derivation of stochastic Schroedinger equations can
be greatly simplified by taking advantage of the existence of this hierarchy of
approximations and its connection to the Ehrenfest theorem. Several examples
are illustrated: the free wave-packet expansion, the Kerr oscillator, a
generalized version of the Kerr oscillator, as well as interacting bosons or
fermions.


title:
Experimental evidence for the breakdown of a Hartree-Fock approach in a
  weakly interacting Bose gas

abstract:
  We study the formation of a quasi-condensate in a nearly one dimensional,
weakly interacting trapped atomic Bose gas. We show that a Hartree Fock
(mean-field) approach fails to explain the presence of the quasi-condensate in
the center of the cloud: the quasi-condensate appears through an
interaction-driven cross-over and not a saturation of the excited states.
Numerical calculations based on Bogoliubov theory give an estimate of the
cross-over density in agreement with experimental results.


title: Properties and Application of Nondeterministic Quantum Query Algorithms

abstract:
  Many quantum algorithms can be analyzed in a query model to compute Boolean
functions where input is given by a black box. As in the classical version of
decision trees, different kinds of quantum query algorithms are possible:
exact, zero-error, bounded-error and even nondeterministic. In this paper, we
study the latter class of algorithms. We introduce a fresh notion in addition
to already studied nondeterministic algorithms and introduce dual
nondeterministic quantum query algorithms. We examine properties of such
algorithms and prove relations with exact and nondeterministic quantum query
algorithm complexity. As a result and as an example of the application of
discovered properties, we demonstrate a gap of n vs. 2 between classical
deterministic and dual nondeterministic quantum query complexity for a specific
Boolean function.


title:
Direct measurement of decoherence for entanglement between a photon and
  stored atomic excitation

abstract:
  Violations of a Bell inequality are reported for an experiment where one of
two entangled qubits is stored in a collective atomic memory for a user-defined
time delay. The atomic qubit is found to preserve the violation of a Bell
inequality for storage times up to 21 microseconds, 700 times longer than the
duration of the excitation pulse that creates the entanglement. To address the
question of the security of entanglement-based cryptography implemented with
this system, an investigation of the Bell violation as a function of the
cross-correlation between the generated nonclassical fields is reported, with
saturation of the violation close to the maximum value allowed by quantum
mechanics.


title: Physical meaning and derivation of Schrodinger and Dirac equations

abstract:
  The wavefunction of a particle is obtained from its intermediate states and
interaction processes considered as happening concurrently. When the
interaction is described by a potential, the energy of the particle is equal to
its total kinetic plus potential energies. We derive the Schrodinger and Dirac
equations as the unique conditions the wavefunction must satisfy at each point
in order to fulfill the corresponding energy equation. PACS numbers: 03.65.-w.
Keywords: Schrodinger equation; Dirac equation; Quantum dynamics.


title:
Quantum state engineering in a cavity by Stark chirped rapid adiabatic
  passage

abstract:
  We propose a robust scheme to generate single-photon Fock states and
atom-photon and atom-atom entanglement in atom-cavity systems. We also present
a scheme for quantum networking between two cavity nodes using an atomic
channel. The mechanism is based on Stark-chirped rapid adiabatic passage
(SCRAP) and half-SCRAP processes in a microwave cavity. The engineering of
these states depends on the design of the adiabatic dynamics through the static
and dynamic Stark shifts.


title: Imaginary Entanglement as Cost of Unitarity

abstract:
  This report is about contradiction between fidelity needed to determine the
entanglement and concomitant noise that always accompanies precise measurement.
  Account of quantum properties of field leads to additional noise caused by
multiple particle creation through nonunitarity of quantum field representation
in embedded sections of space (Unruh noise).
  Causes of quantum noise vanish at leaving off assumption about statistical
independence of detectors. Smearing of detector leads to elimination of causes
of Unruh noise and to emergence of imaginary entanglement of few mode states
caused by overlap of detector sections.


title: Vanishing of electron pair recession at central impact

abstract:
  Identity of electrons leads to description of their states by symmetrical or
anti-symmetrical combination of free coherent states.
  Due to the coordinate uncertainty potential energy of the Coulomb repulsing
is limited from above and so when energy of electrons is large enough,
electrons go through each other, without noticing one another.
  We show existence of set of coherent states for which wave packages recession
vanish - electrons remain close regardless of Coulomb repulsion.


title: Quantum mechanics explained

abstract:
  The physical motivation for the mathematical formalism of quantum mechanics
is made clear and compelling by starting from an obvious fact - essentially,
the stability of matter - and inquiring into its preconditions: what does it
take to make this fact possible?


title: A spatially and temporally localized sub-laser-cycle electron source

abstract:
  We present an experimental and numerical study of electron emission from a
sharp tungsten tip triggered by sub-8 femtosecond low power laser pulses. This
process is non-linear in the laser electric field, and the non-linearity can be
tuned via the DC voltage applied to the tip. Numerical simulations of this
system show that electron emission takes place within less than one optical
period of the exciting laser pulse, so that an 8 fsec 800 nm laser pulse is
capable of producing a single electron pulse of less than 1 fsec duration.
Furthermore, we find that the carrier-envelope phase dependence of the emission
process is smaller than 0.1% for an 8 fsec pulse but is steeply increasing with
decreasing laser pulse duration.


title:
Geometric quantum computation using fictitious spin- 1/2 subspaces of
  strongly dipolar coupled nuclear spins

abstract:
  Geometric phases have been used in NMR, to implement controlled phase shift
gates for quantum information processing, only in weakly coupled systems in
which the individual spins can be identified as qubits. In this work, we
implement controlled phase shift gates in strongly coupled systems, by using
non-adiabatic geometric phases, obtained by evolving the magnetization of
fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The
dynamical phase accumulated during the evolution of the subspaces, is refocused
by a spin echo pulse sequence and by setting the delay of transition selective
pulses such that the evolution under the homonuclear coupling makes a complete
$2\pi$ rotation. A detailed theoretical explanation of non-adiabatic geometric
phases in NMR is given, by using single transition operators. Controlled phase
shift gates, two qubit Deutsch-Jozsa algorithm and parity algorithm in a
qubit-qutrit system have been implemented in various strongly dipolar coupled
systems obtained by orienting the molecules in liquid crystal media.


title: Photon wave functions and quantum interference experiments

abstract:
  We present a general theory to describe two-photon interference, including a
formal description of few photon intereference in terms of single-photon
amplitudes. With this formalism, it is possible to describe both frequency
entangled and separable two-photon interference in terms of single-photon wave
functions. Using this description, we address issues related to the physical
interpretation of two-photon interference experiments. We include a discussion
on how few-photon interference can be interpreted as a bosonic exchange effect,
and how this relates to traditional exchange effects with fermions.


title: Error Exponents in Quantum Hypothesis Testing

abstract:
  This paper has been withdrawn by the author because Lemma 3 is incorrect.
This mistake is crucial in this paper.


title: Gallager Bound of Classical-Quantum Channel Coding


title: On the distinguishability of random quantum states

abstract:
  We develop two analytic lower bounds on the probability of success p of
identifying a state picked from a known ensemble of pure states: a bound based
on the pairwise inner products of the states, and a bound based on the
eigenvalues of their Gram matrix. We use the latter to lower bound the
asymptotic distinguishability of ensembles of n random quantum states in d
dimensions, where n/d approaches a constant. In particular, for almost all
ensembles of n states in n dimensions, p>0.72. An application to distinguishing
Boolean functions (the "oracle identification problem") in quantum computation
is given.


title: Entanglement, purity and energy: Two qubits vs Two modes

abstract:
  We study the relationship between the entanglement, mixedness and energy of
two-qubit and two-mode Gaussian quantum states. We parametrize the set of
allowed states of these two fundamentally different physical systems using
measures of entanglement, mixedness and energy that allow us to compare and
contrast the two systems using a phase diagram. This phase diagram enables one
to clearly identify not only the physically allowed states, but the set of
states connected under an arbitrary quantum operation. We pay particular
attention to the maximally entangled mixed states (MEMS) of each system.
Following this we investigate how efficiently one may transfer entanglement
from two-mode to two-qubit states.


title: Wronskian perturbation theoryWronskian perturbation theory

abstract:
  We develop a perturbation method that generalizes an approach proposed
recently to treat velocity--dependent quantum--mechanical models. In order to
test present approach we apply it to some simple trivial and nontrivial
examples.


title: Entangled mixed-state generation by twin-photon scattering

abstract:
  We report experimental results on mixed-state generation by multiple
scattering of polarization-entangled photon pairs created from parametric
down-conversion. By using a large variety of scattering optical systems we have
experimentally obtained entangled mixed states that lie upon and below the
Werner curve in the linear entropy-tangle plane. We have also introduced a
simple phenomenological model built on the analogy between classical
polarization optics and quantum maps. Theoretical predictions from such model
are in full agreement with our experimental findings.


title:
Vibronic "Rabi resonances" in harmonic and hard-wall ion-traps for
  arbitrary laser intensity and detuning

abstract:
  We investigate laser-driven vibronic transitions of a single two-level atomic
ion in harmonic and hard wall traps. In the Lamb-Dicke regime, for tuned or
detuned lasers with respect to the internal frequency of the ion, and weak or
strong laser intensities, the vibronic transitions occur at well isolated "Rabi
Resonances", where the detuning-adapted Rabi frequency coincides with the level
spacing of the vibrational modes. These vibronic resonances are characterized
as avoided crossings of the dressed levels (eigenvalues of the full
Hamiltonian). Their peculiarities due to symmetry constraints and trapping
potential are also examined.


title:
Trapped Ion Chain as a Neural Network: Error Resistant Quantum
  Computation

abstract:
  We demonstrate the possibility of realizing a neural network in a chain of
trapped ions with induced long range interactions. Such models permit one to
store information distributed over the whole system. The storage capacity of
such network, which depends on the phonon spectrum of the system, can be
controlled by changing the external trapping potential. We analyze the
implementation of error resistant universal quantum information processing in
such systems.


title: Quantum scaling laws in the onset of dynamical delocalization

abstract:
  We study the destruction of dynamical localization, experimentally observed
in an atomic realization of the kicked rotor, by a deterministic Hamiltonian
perturbation, with a temporal periodicity incommensurate with the principal
driving. We show that the destruction is gradual, with well defined scaling
laws for the various classical and quantum parameters, in sharp contrast with
predictions based on the analogy with Anderson localization.

categories: quant-ph cond-mat.other nlin.CD physics.atom-ph


title: Structured Codes Improve the Bennett-Brassard-84 Quantum Key Rate

abstract:
  A central goal in information theory and cryptography is finding simple
characterizations of optimal communication rates subject to various
restrictions and security requirements. Ideally, the optimal key rate for a
quantum key distribution (QKD) protocol would be given by {\em single-letter
formula} involving a simple optimization over a single use of an effective
channel. We explore the possibility of such a formula for one of the simplest
and most widely used QKD protocols--Bennett-Brassard-84 (BB84) with one way
classical post-processing. We show that a conjectured single-letter key-rate
formula is false, uncovering a deep ignorance about asymptotically good private
codes and pointing towards unfortunate complications in the theory of QKD.
These complications are not without benefit--with added complexity comes better
key rates than previously thought possible. We improve the threshold for secure
key generation from a bit error rate of 0.124 to 0.129.


title: Optimal Quantum Measurements of Expectation Values of Observables

abstract:
  Experimental characterizations of a quantum system involve the measurement of
expectation values of observables for a preparable state |psi> of the quantum
system. Such expectation values can be measured by repeatedly preparing |psi>
and coupling the system to an apparatus. For this method, the precision of the
measured value scales as 1/sqrt(N) for N repetitions of the experiment. For the
problem of estimating the parameter phi in an evolution exp(-i phi H), it is
possible to achieve precision 1/N (the quantum metrology limit) provided that
sufficient information about H and its spectrum is available. We consider the
more general problem of estimating expectations of operators A with minimal
prior knowledge of A. We give explicit algorithms that approach precision 1/N
given a bound on the eigenvalues of A or on their tail distribution. These
algorithms are particularly useful for simulating quantum systems on quantum
computers because they enable efficient measurement of observables and
correlation functions. Our algorithms are based on a method for efficiently
measuring the complex overlap of |psi> and U|psi>, where U is an implementable
unitary operator. We explicitly consider the issue of confidence levels in
measuring observables and overlaps and show that, as expected, confidence
levels can be improved exponentially with linear overhead. We further show that
the algorithms given here can typically be parallelized with minimal increase
in resource usage.


title:
An efficient method for scattering problems in open billiards: Theory
  and applications

abstract:
  We present an efficient method to solve scattering problems in
two-dimensional open billiards with two leads and a complicated scattering
region. The basic idea is to transform the scattering region to a rectangle,
which will lead to complicated dynamics in the interior, but simple boundary
conditions. The method can be specialized to closed billiards, and it allows
the treatment of interacting particles in the billiard. We apply this method to
quantum echoes measured recently in a microwave cavity, and indicate, how it
can be used for interacting particles.


title: How Quantum Computers Can Fail

abstract:
  We propose and discuss two postulates on the nature of errors in highly
correlated noisy physical stochastic systems. The first postulate asserts that
errors for a pair of substantially correlated elements are themselves
substantially correlated. The second postulate asserts that in a noisy system
with many highly correlated elements there will be a strong effect of error
synchronization. These postulates appear to be damaging for quantum computers.


title:
Computing Boolean Functions: Exact Quantum Query Algorithms and Low
  Degree Polynomials

abstract:
  In this paper we study the complexity of quantum query algorithms computing
the value of Boolean function and its relation to the degree of algebraic
polynomial representing this function. We pay special attention to Boolean
functions with quantum query algorithm complexity lower than the deterministic
one. Relation between the degree of representing polynomial and potentially
possible quantum algorithm complexity has been already described;
unfortunately, there are few examples of quantum algorithms to illustrate
theoretical evaluation of the complexity. Work in this direction was aimed (1)
to construct effective quantum query algorithms for computing Boolean
functions, (2) to design methods for Boolean function construction with a large
gap between deterministic complexity and degree of representing polynomial. In
this paper we present our results in both directions.


title:
Effects of interatomic interaction on cooperative relaxation of
  two-level atoms

abstract:
  We study effects of direct interatomic interaction on cooperative processes
in atom-photon dynamics. Using a model of two-level atoms with Ising-type
interaction as an example, it is demonstrated that interparticle interaction
combined with atom-field coupling can introduce additional interatomic
correlations acting as a phase synchronizing factor. For the case of weakly
interacting atoms with $J<\hbar\omega_0$, where $J$ is the interparticle
coupling constant and $\omega_0$ is the atomic frequency, dynamical regimes of
cooperative relaxation of atoms are analyzed in Born-Markov approximation both
numerically and using the mean field approximation. We show that interparticle
correlations induced by the direct interaction result in inhibition of
incoherent spontaneous decay leading to the regime of collective pulse
relaxation which differs from superradiance in nature. For superradiant
transition, the synchronizing effect of interatomic interaction is found to
manifest itself in enhancement of superradiance. When the interaction is strong
and $J>\hbar\omega_0$, one-partice one-photon transitions are excluded and
transition to the regime of multiphoton relaxation occurs. Using a simple model
of two atoms in a high-Q single mode cavity we show that such transition is
accompanied by Rabi oscillations involving many-atom multiphoton states.
Dephasing effect of dipole-dipole interaction and solitonic mechanism of
relaxation are discussed.


title: Photon creation in a spherical oscillating cavity

abstract:
  We study the photon creation inside a perfectly conducting, spherical
oscillating cavity. The electromagnetic field inside the cavity is described by
means of two scalar fields which satisfy Dirichlet and (generalized) Neumann
boundary conditions. As a preliminary step, we analyze the dynamical Casimir
effect for both scalar fields. We then consider the full electromagnetic case.
The conservation of angular momentum of the electromagnetic field is also
discussed, showing that photons inside the cavity are created in singlet
states.


title: Deformed Heisenberg algebra with upper bound of momentum value

abstract:
  We consider one dimensional deformed Heisenberg algebra leading to existence
of minimal length for coordinate operator and minimal and maximal uncertainty
of momentum operator. For this algebra an exactly solvable Hamiltonian is
constructed.


title: Prime Factorization in the Duality Computer

abstract:
  We give algorithms to factorize large integers in the duality computer. We
provide three duality algorithms for factorization based on a naive
factorization method, the Shor algorithm in quantum computing, and the Fermat's
method in classical computing. All these algorithms are polynomial in the input
size.


title: Resonant tunneling with zero reflection at the classical velocity

abstract:
  An important aspect of resonant tunneling with a probability of unity (thus
zero reflection) through a finite region with length l is studied. The relation
between the velocity expectation value $<\hat v_{res}>$ restricted to a region
of length l and the tunneling time $\tau_{res}$ through the same region is
calculated. The obtained result is the analogue of the mean velocity in
classical mechanics: The velocity expectation value equals exactly the length
divided by the tunneling time. This result holds for any potential but is
especially relevant for finite periodic potentials and inversion symmetric
potentials where resonances show a tunneling probability of unity.


title: All-Optical Measurement Based QIP in Quantum Dots

abstract:
  Parity measurements on qubits can generate the entanglement resource
necessary for scalable quantum computation. Here we describe a method for fast
optical parity measurements on electron spin qubits within coupled quantum
dots. The measurement scheme, which can be realised with existing technology,
consists of the optical excitation of excitonic states followed by monitored
relaxation. Conditional on the observation of a photon, the system is projected
into the odd/even parity subspaces. Our model incorporates all the primary
sources of error, including detector inefficiency, effects of spatial
separation and non-resonance of the dots, and also unwanted excitations.
Through an analytical treatment we establish that the scheme is robust to such
effects. Two applications are presented: a realisation of a CNOT gate, and a
technique for growing large scale graph states.


title:
On a Geometric Structure of Pure Multi-qubit Quantum States and Its
  Applicability to a Numerical Computation

abstract:
  For one-qubit pure quantum states, it is already proved that the Voronoi
diagrams with respect to two distances -- Euclidean distance and the quantum
divergence -- coincide. This fact is a support for a known method to calculate
the Holevo capacity. To consider an applicability of this method to quantum
states of a higher level system, it is essential to check if the coincidence of
the Voronoi diagrams also occurs. In this paper, we show a negative result for
that expectation. In other words, we mathematically prove that those diagrams
no longer coincide in a higher dimension. That indicates that the method used
in one-qubit case to calculate the Holevo capacity might not be effective in a
higher dimension.


title:
First-order intertwining operators with position dependent mass and
  $\eta$- weak-psuedo-Hermiticity generators

abstract:
  A Hermitian and an anti-Hermitian first-order intertwining operators are
introduced and a class of $\eta$-weak-pseudo-Hermitian position-dependent mass
(PDM) Hamiltonians are constructed. A corresponding reference-target
$\eta$-weak-pseudo-Hermitian PDM -- Hamiltonians' map is suggested. Some
$\eta$-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models
are used as illustrative examples. Energy-levels crossing and flown-away states
phenomena are reported for the resulting Scarf II spectrum. Some of the
corresponding $\eta$-weak-pseudo-Hermitian Scarf II- and
periodic-type-isospectral models (PT -symmetric and non-PT -symmetric) are
given as products of the reference-target map.


title: An Electronic Mach-Zehnder Quantum Eraser

abstract:
  We propose an electronic quantum eraser in which the electrons are injected
into a mesoscopic conductor at the quantum Hall regime. The conductor is
composed of a two-path interferometer which is an electronic analogue of the
optical Mach-Zehnder interferometer, and a quantum point contact detector
capacitively coupled to the interferometer. While the interference of the
output current at the interferometer is shown to be suppressed by the
which-path information, we show that the which-path information is erased by
the zero-frequency cross correlation measurement between the interferometer and
the detector output leads. We also investigate a modified setup in which the
detector is replaced by a two-path interferometer.We show that the path
distinguishability and the visibility of the joint detection can be controlled
in a continuous manner, and satisfy a complementarity relation for the
entangled electrons.


title:
Genuine tripartite entanglement semi-monotone for (2 x 2 x
  n)-dimensional systems

abstract:
  In this paper, we present a new approach to study genuine tripartite
entanglement existing in $(2\times 2\times n)-$dimensional quantum pure states.
By utilizing the approach, we introduce a particular quantity to measure
genuine tripartite entanglement. The quantity is shown to be an entanglement
monotone in 2-dimensional subsystems (semi-monotone) and reaches zero for
separable states and $(2\times 2\times 2)-$dimensional $W$ states, hence is a
good criterion to characterize genuine tripartite entanglement. Furthermore,
the formulation for pure states can be conveniently extended to the case of
mixed states by utilizing the kronecker product approximation technique. As
applications, we give the analytic approximation for weakly mixed states, and
study the genuine tripartite entanglement of two given weakly mixed states.


title:
Strong light-matter coupling: parametric interactions in a cavity and
  free-space

abstract:
  We consider parametric interactions of laser pulses in a coherent macroscopic
ensemble of resonant atoms, which are possible in the strong coupling regime of
light-matter interaction. The spectrum condensation (lasing at collective
vacuum Rabi sidebands) was studied in an active cavity configuration.
Parametric interactions under the strong light-matter coupling were proved even
in free space. In contrast to bichromatic beats in a cavity, they were shown to
appear due to interference between polaritonic wave packets of different group
velocities.


title:
On the minimum number of unitaries needed to describe a random-unitary
  channel

abstract:
  We provide, in an extremely simple way, an upper bound to the minimum number
of unitary operators describing a general random-unitary channel.


title:
Constructions of indecomposable positive maps based on a new criterion
  for indecomposability

abstract:
  We give a criterion for a positive mapping on the space of operators on a
Hilbert space to be indecomposable. We show that this criterion can be applied
to two families of positive maps. These families of maps can then be used to
form separability criteria for bipartite quantum states that can detect the
entanglement of bound entangled quantum states.


title:
A Deterministic and Storable Single-Photon Source Based on Quantum
  Memory

abstract:
  A single photon source is realized with a cold atomic ensemble ($^{87}$Rb
atoms). In the experiment, single photons, which is initially stored in an
atomic quantum memory generated by Raman scattering of a laser pulse, can be
emitted deterministically at a time-delay in control. It is shown that
production rate of single photons can be enhanced by a feedback circuit
considerably while the single-photon quality is conserved. Thus our present
single-photon source is well suitable for future large-scale realization of
quantum communication and linear optical quantum computation.


title: Some new results concerning the vacuum in Dirac Hole Theory

abstract:
  In Dirac's hole theory the vacuum state is generally believed to be the state
of minimum energy. It will be shown that this is not, in fact, the case and
that there must exist states in hole theory with less energy than the vacuum
state. It will be shown that energy can be extracted from the hole theory
vacuum state through the application of an electric field.


title: Tunneling times through barrier with inelasticity

abstract:
  Tunneling delay times of wavepackets in quantum mechanical penetration of
rectangular barriers have long been known to show a perplexing independence
with respect to the width of the barrier. This also has relevence to the
transmission of evanescent waves in optics. Some authors have claimed that in
the presence of absorption or inelastic channels (which they model by taking a
complex barrier potential) this effect no longer exists, in that the time delay
becomes proportional to the barrier width. Taking the point of view that
complex potentials imply non-Hermitian Hamiltonians and are as such fraught
with conceptual pit-falls particularly in connection to problems involving time
evolution, we have constructed a two-channel model which does not suffer from
such maladies in order to examine this issue. We find that the conclusions
arrived at by the earlier authors need to be qualified.


title: The quantum capacity with symmetric side channels

abstract:
  We present an upper bound for the quantum channel capacity that is both
additive and convex. Our bound can be interpreted as the capacity of a channel
for high-fidelity quantum communication when assisted by a family of channels
that have no capacity on their own. This family of assistance channels, which
we call symmetric side channels, consists of all channels mapping symmetrically
to their output and environment. The bound seems to be quite tight, and for
degradable quantum channels it coincides with the unassisted channel capacity.
Using this symmetric side channel capacity, we find new upper bounds on the
capacity of the depolarizing channel. We also briefly indicate an analogous
notion for distilling entanglement using the same class of (one-way) channels,
yielding one of the few entanglement measures that is monotonic under local
operations with one-way classical communication (1-LOCC), but not under the
more general class of local operations with classical communication (LOCC).


title:
Representation reduction and solution space contraction in quasi-exactly
  solvable systems

abstract:
  In quasi-exactly solvable problems partial analytic solution (energy spectrum
and associated wavefunctions) are obtained if some potential parameters are
assigned specific values. We introduce a new class in which exact solutions are
obtained at a given energy for a special set of values of the potential
parameters. To obtain a larger solution space one varies the energy over a
discrete set (the spectrum). A unified treatment that includes the standard as
well as the new class of quasi-exactly solvable problems is presented and few
examples (some of which are new) are given. The solution space is spanned by
discrete square integrable basis functions in which the matrix representation
of the Hamiltonian is tridiagonal. Imposing quasi-exact solvability constraints
result in a complete reduction of the representation into the direct sum of a
finite and infinite component. The finite is real and exactly solvable, whereas
the infinite is complex and associated with zero norm states. Consequently, the
whole physical space contracts to a finite dimensional subspace with
normalizable states.


title: Non-adiabatic Arbitary Geometric Gates in 2-qubit NMR Model

abstract:
  We study a 2-qubit nuclear spin system for realizing an arbitrary geometric
quantum phase gate by means of non-adiabatic operation. A single magnetic pulse
with multi harmonic frequencies is applied to manipulate the quantum states of
2-qubit instantly. Using resonant transition approximation, the time dependent
Hamiltonian of two nuclear spins can be solved analytically. The time evolution
of the wave function is obtained without adiabatic approximation. The
parameters of magnetic pulse, such as the frequency, amplitude, phase of each
harmonic part as well as the time duration of the pulse, are determined for
achieving an arbitrary non-adiabatic geometric phase gate. The derivation of
non-adiabatic geometric controlled phase gates and A-A phase are also
addressed.


title:
The condition for entanglement enhanced information transmission of
  Pauli memory channel

abstract:
  The sufficient condition of entanglement enhanced classical capacity is given
for Pauli memory channel with arbitrary channel parameters. In some special
case the condition is also necessary but fail to be necessary in general. The
theory of majorization and perturbation are used in the proving.