title:
Reply to Comment on ''Quantum key distribution for d-level systems with
  generalized Bell states''

abstract:
  In a recent comment \cite{ch1} it has been claimed that an entangled-based
quantum key distribution protocol proposed in \cite{zhang} and its
generalization to d-level systems in \cite{v1} are insecure against an attack
devised by the authors of the comment. We invalidate the arguments of the
comment and show that the protocols are still secure.


title: Surface Screening in the Casimir Force

abstract:
  We calculate the corrections to the Casimir force between two metals due to
the spatial dispersion of their response functions. We employ model-independent
expressions for the force in terms of the optical coefficients. We express the
non-local corrections to the Fresnel coefficients employing the surface
$d_\perp$ parameter, which accounts for the distribution of the surface
screening charge. Within a self-consistent jellium calculation, spatial
dispersion increases the Casimir force significatively for small separations.
The nonlocal correction has the opposite sign than previously predicted
employing hydrodynamic models and assuming abruptly terminated surfaces.


title:
An algorithm to perform POVMs through Neumark theorem: application to
  the discrimination of non-orthogonal pure quantum states

abstract:
  We consider a protocol to perform the optimal quantum state discrimination of
  $N$ linearly independent non-orthogonal pure quantum states and present a
computational code. Through the extension of the original Hilbert space, it is
possible to perform an unitary operation yielding a final configuration, which
gives the best discrimination without ambiguity by means of von Neumann
measurements. Our goal is to introduce a detailed general mathematical
procedure to realize this task by means of semidefinite programming and norm
minimization.
  The former is used to fix which is the best detection probability amplitude
for each state of the ensemble. The latter determines the matrix which leads
the states to the final configuration. In a final step, we decompose the
unitary transformation in a sequence of two-level rotation matrices.


title: Realizing Ternary Quantum Switching Networks without Ancilla Bits

abstract:
  This paper investigates the synthesis of quantum networks built to realize
ternary switching circuits in the absence of ancilla bits. The results we
established are twofold. The first shows that ternary Swap, ternary Not and
ternary Toffoli gates are universal for the realization of arbitrary $n\times
n$ ternary quantum switching networks without ancilla bits. The second result
proves that all $n\times n$ quantum ternary networks can be generated by Not,
Controlled-Not, Multiply-Two, and Toffoli gates. Our approach is constructive.
key words: ternary quantum logic synthesis, quantum circuit optimization, group
theory.


title:
Nondeterministic testing of Sequential Quantum Logic propositions on a
  quantum computer

abstract:
  In the past few years it has been shown that universal quantum computation
can be obtained by projective measurements alone, with no need for unitary
gates. This suggests that the underlying logic of quantum computing may be an
algebra of sequences of quantum measurements rather than an algebra of products
of unitary operators. Such a Sequential Quantum Logic (SQL) was developed in
the late 70's and has more recently been applied to the consistent histories
framework of quantum mechanics as a possible route to the theory of quantum
gravity. In this letter, I give a method for deciding the truth of a
proposition in SQL with nonzero probability of success on a quantum computer.


title: Nonlocality without inequalities

abstract:
  We prove that every conceivable hidden variable model reproducing the quantum
mechanical predictions of almost any entangled state must necessarily violate
Bell's locality condition. The proof does not involve the consideration of any
Bell inequality but it rests on simple set theoretic arguments and it works for
almost any noncompletely factorizable state vector associated to any number of
particles whose Hilbert spaces have arbitrary dimensionality.


title: Identical particles and entanglement

abstract:
  We review two general criteria for deciding whether a pure bipartite quantum
state describing a system of two identical particles is entangled or not. The
first one considers the possibility of attributing a complete set of objective
properties to each particle belonging to the composed system, while the second
is based both on the consideration of the Slater-Schmidt number of the
fermionic and bosonic analog of the Schmidt decomposition and on the evaluation
of the von Neumann entropy of the one-particle reduced statistical operators.


title: A new algorithm for producing quantum circuits using KAK decompositions

abstract:
  We provide a new algorithm that translates a unitary matrix into a quantum
circuit according to the G=KAK theorem in Lie group theory. With our algorithm,
any matrix decomposition corresponding to type-AIII KAK decompositions can be
derived according to the given Cartan involution. Our algorithm contains, as
its special cases, Cosine-Sine decomposition (CSD) and Khaneja-Glaser
decomposition (KGD) in the sense that it derives the same quantum circuits as
the ones obtained by them if we select suitable Cartan involutions and square
root matrices. The selections of Cartan involutions for computing CSD and KGD
will be hown explicitly. As an example, we show explicitly that our method can
automatically reproduce the well-known efficient quantum circuit for the
n-qubit quantum Fourier transform.


title: Effective Spin Quantum Phases in Systems of Trapped Ions

abstract:
  A system of trapped ions under the action of off--resonant standing--waves
can be used to simulate a variety of quantum spin models. In this work, we
describe theoretically quantum phases that can be observed in the simplest
realization of this idea: quantum Ising and XY models. Our numerical
calculations with the Density Matrix Renormalization Group method show that
experiments with ion traps should allow one to access general properties of
quantum critical systems. On the other hand, ion trap quantum spin models show
a few novel features due to the peculiarities of induced effective spin--spin
interactions which lead to interesting effects like long--range quantum
correlations and the coexistence of different spin phases.


title: Control of photon correlations in type II parametric down-conversion

abstract:
  In this paper we describe theoretically quantum control of temporal
correlations of entangled photons produced by collinear type II spontaneous
parametric down-conversion. We examine the effect of spectral phase modulation
of the signal or idler photons arriving at a 50/50 beam splitter on the
temporal shape of the entangled-photon wave packet . The coincidence count rate
is calculated analytically for photon pairs in terms of the modulation depth
applied to either the signal or idler beam with a spectral phase filter. It is
found that the two-photon coincidence rate can be controlled by varying the
modulation depth of the spectral filter.


title: Minimal Bell-Kochen-Specker proofs with POVMs on qubits

abstract:
  There are many different definitions of what a Bell-Kochen-Specker proof with
POVMs might be. Here we present and discuss the minimal proof on qubits for
three of these definitions and show that they are indeed minimal.


title: A Bose-Einstein condensate bouncing off a rough mirror

abstract:
  We present experimental results and theoretical analysis of the diffuse
reflection of a Bose-Einstein condensate from a rough mirror. The mirror is
produced by a blue-detuned evanescent wave supported by a dielectric substrate.
The results are carefully analysed via a comparison with a numerical
simulation. The scattering is clearly anisotropic, more pronounced in the
direction of the evanescent wave surface propagation, as predicted
theoretically.


title: Qubits entanglement dynamics modified by an effective atomic environment

abstract:
  We study entanglement dynamics of a couple of two-level atoms resonantly
interacting with a cavity mode and embedded in a dispersive atomic environment.
We show that in the absence of the environment the entanglement reaches its
maximum value when only one exitation is involved. Then, we find that the
atomic environment modifies that entanglement dynamics and induces a typical
collapse-revival structure even for an initial one photon Fock state of the
field.


title: Quantum Computation by Communication

abstract:
  We present a new approach to scalable quantum computing--a ``qubus
computer''--which realises qubit measurement and quantum gates through
interacting qubits with a quantum communication bus mode. The qubits could be
``static'' matter qubits or ``flying'' optical qubits, but the scheme we focus
on here is particularly suited to matter qubits. There is no requirement for
direct interaction between the qubits. Universal two-qubit quantum gates may be
effected by schemes which involve measurement of the bus mode, or by schemes
where the bus disentangles automatically and no measurement is needed. In
effect, the approach integrates together qubit degrees of freedom for
computation with quantum continuous variables for communication and
interaction.


title: Fault-tolerance threshold for a distance-three quantum code

abstract:
  The quantum error threshold is the highest (model-dependent) noise rate which
we can tolerate and still quantum-compute to arbitrary accuracy. Although noise
thresholds are frequently estimated for the Steane seven-qubit, distance-three
quantum code, there has been no proof that a constant threshold even exists for
distance-three codes. We prove the existence of a constant threshold. The
proven threshold is well below estimates, based on simulations and analytic
models, of the true threshold, but at least it is now known to be positive.


title: Direct measurement of finite-time disentanglement induced by a reservoir

abstract:
  We propose a method for directly probing the dynamics of disentanglement of
an initial two-qubit entangled state, under the action of a reservoir. We show
that it is possible to detect disentanglement, for experimentally realizable
examples of decaying systems, through the measurement of a single observable,
which is invariant throughout the decay. The systems under consideration may
lead to either finite-time or asymptotic disentanglement. A general
prescription for measuring this observable, which yields an operational meaning
to entanglement measures, is proposed, and exemplified for cavity quantum
electrodynamics and trapped ions.


title:
Continuous Non-Demolition Observation, Quantum Filtering and Optimal
  Estimation

abstract:
  A quantum stochastic model for an open dynamical system (quantum receiver)
and output multi-channel of observation with an additive nonvacuum quantum
noise is given. A quantum stochastic Master equation for the corresponding
instrument is derived and quantum stochastic filtering equations both for the
Heisenberg operators and the reduced density matrix of the system under the
nondemolition observation are found. Thus the dynamical problem of quantum
filtering is generalized for a noncommutative output process, and a quantum
stochastic model and optimal filtering equation for the dynamical estimation of
an input Markovian process is found. The results are illustrated on an example
of optimal estimation of an input Gaussian diffusion signal, an unknown
gravitational force say in a quantum optical or Weber's antenna for detection
and filtering a gravitational waves.


title: Quantum Algorithm for Commutativity Testing of a Matrix Set

abstract:
  Suppose we have k matrices of size n by n. We are given an oracle that knows
all the entries of k matrices, that is, we can query the oracle an (i,j) entry
of the l-th matrix. The goal is to test if each pair of k matrices commute with
each other or not with as few queries to the oracle as possible. In order to
solve this problem, we use a theorem of Mario Szegedy (quant-ph/0401053) that
relates a hitting time of a classical random walk to that of a quantum walk. We
also take a look at another method of quantum walk by Andris Ambainis
(quant-ph/0311001). We apply both walks into triangle finding problem
(quant-ph/0310134) and matrix verification problem (quant-ph/0409035) to
compare the powers of the two different walks. We also present Ambainis's
method of lower bounding technique (quant-ph/0002066) to obtain a lower bound
for this problem. It turns out Szegedy's algorithm can be generalized to solve
similar problems. Therefore we use Szegedy's theorem to analyze the problem of
matrix set commutativity. We give an O(k^{4/5}n^{9/5}) algorithm as well as a
lower bound of Omega(k^{1/2}n). We generalize the technique used in coming up
with the upper bound to solve a broader range of similar problems. This is
probably the first problem to be studied on the quantum query complexity using
quantum walks that involves more than one parameter, here, k and n.


title: Quantum Entanglement in the Two Impurity Kondo Model

abstract:
  In order to quantify quantum entanglement in two impurity Kondo systems, we
calculate the concurrence, negativity, and von Neumann entropy. The
entanglement of the two Kondo impurities is shown to be determined by two
competing many-body effects, the Kondo effect and the
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, $I$. Due to the
spin-rotational invariance of the ground state, the concurrence and negativity
are uniquely determined by the spin-spin correlation between the impurities. It
is found that there exists a critical minimum value of the antiferromagnetic
correlation between the impurity spins which is necessary for entanglement of
the two impurity spins. The critical value is discussed in relation with the
unstable fixed point in the two impurity Kondo problem. Specifically, at the
fixed point there is no entanglement between the impurity spins. Entanglement
will only be created (and quantum information processing (QIP) be possible) if
the RKKY interaction exchange energy, $I$, is at least several times larger
than the Kondo temperature, $T_K$. Quantitative criteria for QIP are given in
terms of the impurity spin-spin correlation.


title: Non-Markovian dynamics of a qubit

abstract:
  In this paper we investigate the non-Markovian dynamics of a qubit by
comparing two generalized master equations with memory. In the case of a
thermal bath, we derive the solution of the post-Markovian master equation
recently proposed in Ref. [A. Shabani and D.A. Lidar, Phys. Rev. A {\bf 71},
020101(R) (2005)] and we study the dynamics for an exponentially decaying
memory kernel. We compare the solution of the post-Markovian master equation
with the solution of the typical memory kernel master equation. Our results
lead to a new physical interpretation of the reservoir correlation function and
bring to light the limits of usability of master equations with memory for the
system under consideration.


title: Brokered Graph State Quantum Computing

abstract:
  We describe a procedure for graph state quantum computing that is tailored to
fully exploit the physics of optically active multi-level systems. Leveraging
ideas from the literature on distributed computation together with the recent
work on probabilistic cluster state synthesis, our model assigns to each
physical system two logical qubits: the broker and the client. Groups of
brokers negotiate new graph state fragments via a probabilistic optical
protocol. Completed fragments are mapped from broker to clients via a simple
state transition and measurement. The clients, whose role is to store the
nascent graph state long term, remain entirely insulated from failures during
the brokerage. We describe an implementation in terms of NV-centres in diamond,
where brokers and clients are very naturally embodied as electron and nuclear
spins.


title:
Observables of Angular Momentum as Observables on the Fedosov Quantized
  Sphere

abstract:
  In this paper we construct the commutators of the Fedosov * (a generalization
of the Moyal star product) on the phase space of S2. It is shown that this
product obeys the standard angular momentum commutation relations in ordinary
nonrelativistic quantum mechanics. The purpose of this paper is three-fold. One
is to find an exact, non-perturbative solution to the commutators of the
Fedosov *. The other is to verify that these commutation relations correspond
to angular momentum commutation relations as in ordinary nonrelativistic
quantum mechanics. The last is to show a more general computation of the
Fedosov *; essentially undeforming Fedosov's algorithm.


title: Expanded Conclusive Eavesdropping in Quantum Key Distribution

abstract:
  The paper [Howard E. Brandt, "Conclusive eavesdropping in quantum key
distribution," J. Opt. B: Quantum Semiclass. Opt. 7 (2005)] is generalized to
include the full range of error rates for the projectively measured quantum
cryptographic entangling probe, and also the full range of inconclusive rates
for the entangling probe measured with the POVM receiver.


title: Unambiguous unitary quantum channels

abstract:
  Unambiguous unitary maps and unambiguous unitary quantum channels are
introduced and some of their properties are derived. These properties ensure
certain simple form for the measurements involved in realizing an unambiguous
unitary quantum channel. Error correction and unambiguous error correction with
nonzero probability are discussed in terms of unambiguous unitary quantum
channels. We not only re-derive the well-known condition for a set of errors to
be correctable with certainty, but also obtain a necessary and sufficient
condition for the errors caused by a noisy channel to be correctable with any
nonzero probability. Dense coding with a partially entangled state can also be
viewed as an unambiguous unitary quantum channel when all messages are required
to be transmitted with equal probability of success, the maximal achievable
probability of success is derived and the optimum protocol is also obtained.


title:
Statistical Reconstruction of arbitrary spin states of particles: root
  approach

abstract:
  A method of quantum tomography of arbitrary spin particle states is developed
on the basis of the root approach. It is shown that the set of mutually
complementary distributions of angular momentum projections can be naturally
described by a set of basis functions based on the Kravchuk polynomials. The
set of Kravchuk basis functions leads to a multi-parametric statistical
distribution that generalizes the binomial distribution. In order to analyze a
statistical inverse problem of quantum mechanics, we investigated the
likelihood equation and the statistical properties of the obtained estimates.
The conclusions of the analytical researches are approved by the results of
numerical calculations.


title: What is "system": some decoherence-theory arguments

abstract:
  We discuss the possibility of making the {\it initial} definitions of
mutually different (possibly interacting, or even entangled) systems in the
context of decoherence theory. We point out relativity of the concept of
elementary physical system as well as point out complementarity of the
different possible divisions of a composite system into "subsystems", thus
eventually sharpening the issue of 'what is system'.


title: Comment on "Time-dependent entropy of simple quantum model systems"

abstract:
  In the above mentioned paper by J. Dunkel and S. A. Trigger [Phys. Rev. {\bf
A 71}, 052102, (2005)] a hypothesis has been pursued that the loss of
information associated with the quantum evolution of pure states, quantified in
terms of an increase in time of so-called Leipnik's joint entropy, could be a
rather general property shared by many quantum systems. This behavior has been
confirmed for the unconfined model systems and properly tuned initial data
(maximally classical states). We provide two particular examples which indicate
a complexity of the quantum evolution. In the presence of a confining
(harmonic) potential Leipnik's entropy may be non-increasing for maximally
classical initial data. Another choice of initial data implies periodicity in
time of the Leipnik entropy.


title: On the Quantum Mechanics for One Photon

abstract:
  This paper revisits the quantum mechanics for one photon from the modern
viewpoint and by the geometrical method. Especially, besides the ordinary
(rectangular) momentum representation, we provide an explicit derivation for
the other two important representations, called the cylindrically symmetrical
representation and the spherically symmetrical representation, respectively.
These other two representations are relevant to some current photon experiments
in quantum optics. In addition, the latter is useful for us to extract the
information on the quantized black holes. The framework and approach presented
here are also applicable to other particles with arbitrary mass and spin, such
as the particle with spin 1/2.


title: Teleporting a quantum state in a subset of the whole Hilbert space

abstract:
  We investigate the lower bound of the amount of entanglement for faithfully
teleporting a quantum state belonging to a subset of the whole Hilbert space.
Moreover, when the quantum state belongs to a set composed of two states, a
probabilistic teleportation scheme is presented using a non-maximally entangled
state as the quantum channel. We also calculate the average transmission
efficiency of this scheme.


title: N-qubit entanglement via the $J_y^2$-type collective interaction

abstract:
  We investigate quantum correlations of the $N$-qubit states via a collective
pseudo-spin interaction ($\propto J_y^2$) on arbitrary pure separable states
for a given interval of time. Based on this dynamical generation of the
$N$-qubit maximal entangled states, a quantum secret sharing protocol with $N$
continuous classical secrets is developed.


title:
Phase-stable source of polarization-entangled photons using a
  polarization Sagnac interferometer

abstract:
  We demonstrate a simple, robust, and ultrabright parametric down-conversion
source of polarization-entangled photons based on a polarization Sagnac
interferometer. Bidirectional pumping in type-II phase-matched periodically
poled KTiOPO4 yields a measured flux of 5 000 polarization-entangled pairs/s
per mW of pump power in a 1-nm bandwidth at 96.8% quantum-interference
visibility. The common-path arrangement of the Sagnac interferometer eliminates
the need for phase stabilization for the biphoton output state.


title:
Macroscopic quantum information channel via the polarization-sensitive
  interaction between the light and spin subsystems

abstract:
  We discuss the quantum information channel, which is based on coherent and
polarization sensitive interaction of light and atomic spin waves. We show that
the joint Heisenberg dynamics of the polarization Stokes components of light
and of the angular momenta of atoms has a wave nature and can be properly
described in terms of the macroscopic polariton-type spin wave created in the
sample. The principles of the quantum memory and readout protocols via the wave
coupling of the output time modes in the light subsystem and the output spatial
modes in the spin subsystem are demonstrated.


title: Quantum kinetics of refocusing

abstract:
  We consider quantum kinetics of an open quantum system in the presence of
periodic fields designed to suppress the internal evolution and shield the
system from generic low-frequency environment (refocusing or dynamical
decoupling in application to multi-qubit systems). Assuming that the refocusing
has order K, that is, for frozen environment the cumulant expansion of the
evolution operator over the period tau begins with the term ~tau^(K+1), we
trace the associated cancellations in the kernel of the quantum kinetic
equation in the Floquet formalism and characterize the remaining decoherence
processes.


title: The Blackbody Radiation in D-Dimensional Universes

abstract:
  The blackbody radiation is analyzed in universes with $D$ spatial dimensions.
With the classical electrodynamics suited to the universe in focus and
recurring to the hyperspherical coordinates, it is shown that the spectral
energy density as well as the total energy density are sensible to the
dimensionality of the universe. Wien's displacement law and the
Stefan-Boltzmann law are properly generalized.


title:
The peremptory influence of a uniform background for trapping neutral
  fermions with an inversely linear potential

abstract:
  The problem of neutral fermions subject to an inversely linear potential is
revisited. It is shown that an infinite set of bound-state solutions can be
found on the condition that the fermion is embedded in an additional uniform
background potential. An apparent paradox concerning the uncertainty principle
is solved by introducing the concept of effective Compton wavelength.


title: Reliably distinguishing states in qutrit channels using one-way LOCC

abstract:
  We present numerical evidence showing that any three-dimensional subspace of
C^3 \otimes C^n has an orthonormal basis which can be reliably distinguished
using one-way LOCC, where a measurement is made first on the 3-dimensional part
and the result used to select an optimal measurement on the n-dimensional part.
This conjecture has implications for the LOCC-assisted capacity of certain
quantum channels, where coordinated measurements are made on the system and
environment. By measuring first in the environment, the conjecture would imply
that the environment-assisted classical capacity of any rank three channel is
at least log 3. Similarly by measuring first on the system side, the conjecture
would imply that the environment-assisting classical capacity of any qutrit
channel is log 3. We also show that one-way LOCC is not symmetric, by providing
an example of a qutrit channel whose environment-assisted classical capacity is
less than log 3.


title:
Generation of a highly phase sensitive polarization squeezed N-photon
  state by collinear parametric downconversion and coherent photon subtraction

abstract:
  It is shown that a highly phase sensitive polarization squeezed (2n-1)-photon
state can be generated by subtracting a diagonally polarized photon from the 2n
photon component generated in collinear type II downconversion. This
polarization wedge state has the interesting property that its photon number
distribution in the horizontal and vertical polarizations remains sharply
defined for phase shifts of up to 1/n between the circularly polarized
components. Phase shifts at the Heisenberg limit are therefore observed as
nearly deterministic transfers of a single photon between the horizontal and
vertical polarization components.


title: Unravelling Entanglement

abstract:
  We show that the time evolution of entanglement under incoherent environment
coupling can be faithfully recovered by monitoring the system according to a
suitable measurement scheme.


title: Two-setting Bell Inequalities for Graph States

abstract:
  We present Bell inequalities for graph states with high violation of local
realism. In particular, we show that there is a two-setting Bell inequality for
every nontrivial graph state which is violated by the state at least by a
factor of two. These inequalities are facets of the convex polytope containing
the many-body correlations consistent with local hidden variable models. We
first present a method which assigns a Bell inequality for each graph vertex.
Then for some families of graph states composite Bell inequalities can be
constructed with a violation of local realism increasing exponentially with the
number of qubits. We also suggest a systematic way for obtaining Bell
inequalities with a high violation of local realism for arbitrary graphs.


title: Laser control for the optimal evolution of pure quantum states

abstract:
  Starting from an initial pure quantum state, we present a strategy for
reaching a target state corresponding to the extremum (maximum or minimum) of a
given observable. We show that a sequence of pulses of moderate intensity,
applied at times when the average of the observable reaches its local or global
extremum, constitutes a strategy transferable to different control issues.
Among them, post-pulse molecular alignment and orientation are presented as
examples. The robustness of such strategies with respect to experimentally
relevant parameters is also examined.


title: Performance Analysis for Brandt's Conclusive Entangling Probe

abstract:
  The Fuchs-Peres-Brandt (FPB) probe realizes the most powerful individual
attack on Bennett-Brassard 1984 quantum key distribution by means of a single
controlled-NOT gate in which Alice's transmitted qubit becomes the
control-qubit input, Bob's received qubit is the control-qubit output, and Eve
supplies the target-qubit input and measures the target-qubit output. The FPB
probe uses the minimum-error-probability projective measurement for
discriminating between the target-qubit output states that are perfectly
correlated with Bob's sifted bit value when that bit is correctly received.
This paper analyzes a recently proposed modification of the FPB attack in which
Eve's projective measurement is replaced by a probability operator-valued
measurement chosen to unambiguously discriminate between the same two
target-qubit output states.


title:
Three Dimensional Time Theory: to Unify the Principles of Basic Quantum
  Physics and Relativity

abstract:
  Interpreting quantum mechanics(QM) by classical physics seems like an old
topic; And unified theory is in physics frontier; But because the principles of
quantum physics and relativity are so different, any theories of trying to
unify 4 nature forces should not be considered as completed without truly
unifying the basic principles between QM and relativity. This paper will
interpret quantum physics by using two extra dimensional time as quantum hidden
variables. I'll show that three dimensional time is a bridge to connect basics
quantum physics, relativity and string theory. ``Quantum potential'' in Bohm's
quantum hidden variable theory is derived from Einstein Lagrangian in
6-dimensional time-space geometry. Statistical effect in the measurement of
single particle, non-local properties, de Broglie wave can be naturally derived
from the natural properties of three dimensional time. Berry phase, double-slit
interference of single particle, uncertainty relation, wave-packet collapse are
discussed. The spin and g factor are derived from geometry of extra two time
dimensions. Electron can be expressed as time monopole. In the last part of
this paper, I'll discuss the relation between three dimensional time and
unified theory.
  Key words: Quantum hidden variable, Interpreting of quantum physics, Berry
phase, three dimensional time, unified theory


title: Noise Secured Internet

abstract:
  This work shows how a secure Internet can be implemented through a fast key
distribution system that uses physical noise to protect the transmitted
information. Starting from a shared random sequence $K_0$ between two (or more)
users, longsequences $R$ of random bits can be shared. The signals sent over
the Internet are deterministic but have a built-in Nature-made uncertainty that
protects the shared sequences. After privacy amplification the shared $R$
random bits --encrypted by noise-- are subsequently utilized in one-time-pad
data ciphering.


title:
Noncommuting vector fields, polynomial approximations and control of
  inhomogeneous quantum ensembles

abstract:
  Finding control fields (pulse sequences) that can compensate for the
dispersion in the parameters governing the evolution of a quantum system is an
important problem in coherent spectroscopy and quantum information processing.
The use of composite pulses for compensating dispersion in system dynamics is
widely known and applied. In this paper, we make explicit the key aspects of
the dynamics that makes such a compensation possible. We highlight the role of
Lie algebras and non-commutativity in the design of a compensating pulse
sequence. Finally we investigate three common dispersions in NMR spectroscopy,
the Larmor dispersion, rf-inhomogeneity and strength of couplings between the
spins.


title: Quantum Nonlocality of N-qubit W states

abstract:
  An experimental setup for testing quantum nonlocality of N qubits is
proposed. This method is a generalization of the optical setup proposed by
Banaszek and Wodkiewicz [1]. The quantum nonlocality of N qubits can be
obtained through its violation of N-qubit Bell inequalities. The correlation
function measured in the experiment is described by the Wigner function. The
effect of inefficient detector is also considered.


title: Precision of single-qubit gates based on Raman transitions

abstract:
  We analyze the achievable precision for single-qubit gates that are based on
Raman transitions between two near-degenerate ground states via a virtually
excited state. In particular, we study the errors due to non-perfect
adiabaticity and due to spontaneous emission from the excited state. For the
case of non-adabaticity, we calculate the error as a function of the
dimensionless parameter $\chi=\Delta \tau$, where $\Delta$ is the detuning of
the Raman beams and $\tau$ is the gate time. For the case of spontaneous
emission, we give an analytical argument that the gate errors are approximately
equal to $\Lambda \gamma/\Delta$, where $\Lambda$ is the rotation angle of the
one-qubit gate and $\gamma$ is the spontaneous decay rate, and we show
numerically that this estimate holds to good approximation.


title: Unambiguous pure state identification without classical knowledge

abstract:
  We study how to unambiguously identify a given quantum pure state with one of
the two reference pure states when no classical knowledge on the reference
states is given but a certain number of copies of each reference quantum state
are presented. By the unambiguous identification, we mean that we are not
allowed to make a mistake but our measurement can produce an inconclusive
result. Assuming the two reference states are independently distributed over
the whole pure state space in a unitary invariant way, we determine the optimal
mean success probability for an arbitrary number of copies of the reference
states and a general dimension of the state space. It is explicitly shown that
the obtained optimal mean success probability asymptotically approaches that of
the unambiguous discrimination as the number of the copies of the reference
states increases.


title: Understanding entangled spins in QED

abstract:
  The stability of two entangled spins dressed by electrons is studied by
calculating the scattering phase shifts. The interaction between electrons is
interpreted by fully relativistic QED and the screening effect is described
phenomenologically in the Debye exponential form $e^{-\alpha r}$. Our results
show that if the (Einstein-Podolsky-Rosen-) EPR-type states are kept stable
under the interaction of QED, the spatial wave function must be
parity-dependent. The spin-singlet state $s=0$ and the polarized state $\frac
1{\sqrt{2}}(\mid +-> -\mid -+>)$ along the z-axis\QTR{bf}{\}give rise to two
different kinds of phase shifts\QTR{bf}{.} Interestingly, the interaction
between electrons in the spin-singlet pair is found to be attractive. Such an
attraction could be very useful when we extract the entangled spins from
superconductors. A mechanism to filter the entangled spins is also discussed.


title: Entanglement-induced state ordering under local operations

abstract:
  We analyze how entanglement between two components of a bipartite system
behaves under the action of local channels of the form $\cE\otimes\cI$. We show
that a set of maximally entangled states is by the action of $\cE\otimes\cI$
transformed into the set of states that exhibit the same degree of
entanglement. Moreover, this degree represents an upper bound on entanglement
that is available at the output of the channel irrespective what is the input
state of the composite system. We show that within this bound the the
entanglement-induced state ordering is ``relative'' and can be changed by the
action of local channels. That is, two states $\varrho_1^{(in)}$ and
$\varrho_2^{(in)}$ such that the entanglement $E[\varrho_1^{(in)}]$ of the
first state is larger than the entanglement $E[\varrho_2^{(in)}]$ of the second
state are transformed into states $\varrho_1^{(out)}$ and $\varrho_2^{(out)}$
such that $E[\varrho_2^{(out)}] > E[\varrho_1^{(out)}]$.


title: WKB approximation in deformed space with minimal length

abstract:
  The WKB approximation for deformed space with minimal length is considered.
The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in
presence of deformation is that the WKB approximation is valid for intermediate
quantum numbers and can be invalid for small as well as very large quantum
numbers. The correctness of the rule is verified by comparing obtained results
with exact expressions for corresponding spectra.


title: Detection of N-particle entanglement with generalized Bell inequalities

abstract:
  We show that the generalized Bell-type inequality, explicitly involving
rotational symmetry of physical laws, is very efficient in distinguishing
between true N-particle quantum correlations and correlations involving less
particles. This applies to various types of generalized partial separabilities.
We also give a rigorous proof that the new Bell inequalities are maximally
violated by the GHZ states, and find a very handy description of the N-qubit
correlation function.


title: Incoherent control and entanglement for two-dimensional coupled systems

abstract:
  We investigate accessibility and controllability of a quantum system S
coupled to a quantum probe P, both described by two-dimensional Hilbert spaces,
under the hypothesis that the external control affects only P. In this context
accessibility and controllability properties describe to what extent it is
possible to drive the state of the system S by acting on P and using the
interaction between the two systems. We give necessary and sufficient
conditions for these properties and we discuss the relation with the entangling
capability of the interaction between S and P. In particular, we show that
controllability can be expressed in terms of the SWAP operator, acting on the
composite system, and its square root.


title: Quantum Error Correction of a Qubit Loss in an Addressable Atomic System

abstract:
  We present a scheme for correcting qubit loss error while quantum computing
with neutral atoms in an addressable optical lattice. The qubit loss is first
detected using a quantum non-demolition measurement and then transformed into a
standard qubit error by inserting a new atom in the vacated lattice site. The
logical qubit, encoded here into four physical qubits with the
Grassl-Beth-Pellizzari code, is reconstructed via a sequence of one projective
measurement, two single-qubit gates, and three controlled-NOT operations. No
ancillary qubits are required. Both quantum non-demolition and projective
measurements are implemented using a cavity QED system which can also detect a
general leakage error and thus allow qubit loss to be corrected within the same
framework. The scheme can also be applied in quantum computation with trapped
ions or with photons.


title:
Entanglement verification for quantum key distribution systems with an
  underlying bipartite qubit-mode structure

abstract:
  We consider entanglement detection for quantum key distribution systems that
use two signal states and continuous variable measurements. This problem can be
formulated as a separability problem in a qubit-mode system. To verify
entanglement, we introduce an object that combines the covariance matrix of the
mode with the density matrix of the qubit. We derive necessary separability
criteria for this scenario. These criteria can be readily evaluated using
semidefinite programming and we apply them to the specific quantum key
distribution protocol.


title: Semiclassical coherent state propagator for systems with spin

abstract:
  We derive the semiclassical limit of the coherent state propagator for
systems with two degrees of freedom of which one degree of freedom is canonical
and the other a spin. Systems in this category include those involving
spin-orbit interactions and the Jaynes-Cummings model in which a single
electromagnetic mode interacts with many independent two-level atoms. We
construct a path integral representation for the propagator of such systems and
derive its semiclassical limit. As special cases we consider separable systems,
the limit of very large spins and the case of spin 1/2.


title: A new perturbative approach to the adiabatic approximation

abstract:
  A new and intuitive perturbative approach to time-dependent quantum mechanics
problems is presented, which is useful in situations where the evolution of the
Hamiltonian is slow. The state of a system which starts in an instantaneous
eigenstate of the initial Hamiltonian is written as a power series which has a
straightforward diagrammatic representation. Each term of the series
corresponds to a sequence of "adiabatic" evolutions, during which the system
remains in an instantaneous eigenstate of the Hamiltonian, punctuated by
transitions from one state to another. The first term of this series is the
standard adiabatic evolution, the next is the well-known first correction to
it, and subsequent terms can be written down essentially by inspection.
Although the final result is perhaps not terribly surprising, it seems to be
not widely known, and the interpretation is new, as far as we know. Application
of the method to the adiabatic approximation is given, and some discussion of
the validity of this approximation is presented.


title: On the performance of two protocols: SARG04 and BB84

abstract:
  We compare the performance of BB84 and SARG04, the later of which was
proposed by V. Scarani et al., in Phys. Rev. Lett. 92, 057901 (2004).
Specifically, in this paper, we investigate SARG04 with two-way classical
communications and SARG04 with decoy states. In the first part of the paper, we
show that SARG04 with two-way communications can tolerate a higher bit error
rate (19.4% for a one-photon source and 6.56% for a two-photon source) than
SARG04 with one-way communications (10.95% for a one-photon source and 2.71%
for a two-photon source). Also, the upper bounds on the bit error rate for
SARG04 with two-way communications are computed in a closed form by considering
an individual attack based on a general measurement. In the second part of the
paper, we propose employing the idea of decoy states in SARG04 to obtain
unconditional security even when realistic devices are used. We compare the
performance of SARG04 with decoy states and BB84 with decoy states. We find
that the optimal mean-photon number for SARG04 is higher than that of BB84 when
the bit error rate is small. Also, we observe that SARG04 does not achieve a
longer secure distance and a higher key generation rate than BB84, assuming a
typical experimental parameter set.


title: Levinson's theorem and reflectionless one-dimensional potentials

abstract:
  We studied two possible approaches to one-dimensional Levinson's theorem for
Sch\"odinger equation. The first one, we restrict the 3-dimensional theorem.
The other one, the theorem proposed by Dong, Ma and Klauss \cite{Dong}. We find
failures in each approach for a one-dimensional reflectionless potential. In
order to see this, we explicitly evaluate the phase shift using Schr\"odinger
equation using solution procedure proposed by Jaffe \cite{Jaffe}.


title: Simulating lattice gauge theories on a quantum computer

abstract:
  We examine the problem of simulating lattice gauge theories on a universal
quantum computer. The basic strategy of our approach is to transcribe lattice
gauge theories in the Hamiltonian formulation into a Hamiltonian involving only
Pauli spin operators such that the simulation can be performed on a quantum
computer using only one and two qubit manipulations. We examine three models,
the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a
spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the
lattice. The number of qubits required for storing a particular state is found
to have a linear dependence with the total number of lattice sites. The number
of qubit operations required for performing the time evolution corresponding to
the Hamiltonian is found to be between a linear to quadratic function of the
number of lattice sites, depending on the arrangement of qubits in the quantum
computer. We remark that our results may also be easily generalized to higher
SU(N) gauge theories.


title: Quantum Diffusion, Measurement and Filtering

abstract:
  A brief presentation of the basic concepts in quantum probability theory is
given in comparison to the classical one. The notion of quantum white noise,
its explicit representation in Fock space, and necessary results of
noncommutative stochastic analysis and integration are outlined. Algebraic
differential equations that unify the quantum non Markovian diffusion with
continuous non demolition observation are derived. A stochastic equation of
quantum diffusion filtering generalising the classical Markov filtering
equation to the quantum flows over arbitrary *-algebra is obtained. A Gaussian
quantum diffusion with one dimensional continuous observation is considered.The
a posteriori quantum state difusion in this case is reduced to a linear quantum
stochastic filter equation of Kalman-Bucy type and to the operator Riccati
equation for quantum correlations. An example of continuous nondemolition
observation of the coordinate of a free quantum particle is considered,
describing a continuous collase to the stationary solution of the linear
quantum filtering problem found in the paper.


title: Teleportation and Dense Coding with Genuine Multipartite Entanglement

abstract:
  We present an explicit protocol ${\cal E}_0$ for faithfully teleporting an
arbitrary two-qubit state via a genunie four-qubit entangled state. By
construction, our four-partite state is not reducible to a pair of Bell states.
Its properties are compared and contrasted with those of the four-party GHZ and
W states. We also give a dense coding scheme ${\cal D}_0$ involving our state
as a shared resource of entanglement. Both ${\cal D}_0$ and ${\cal E}_0$
indicate that our four-qubit state is a likely candidate for the genunine
four-partite analogue to a Bell state.


title: The world of quantum noise and the fundamental output process

abstract:
  A stationary theory of quantum stochastic processes of second order is
outlined. It includes KMS processes in wide sense like the equilibrium finite
temperature quantum noise given by the Planck's spectral formula. It is shown
that for each stationary noise there exists a natural output process output
process which is identical to the noise in the infinite temperature limit, and
flipping with the noise if the time is reversed at finite temperature. A
canonical Hilbert space representation of the quantum noise and the fundamental
output process is established and a decomposition of their spectra is found. A
brief explanation of quantum stochastic integration with respect to the
input-output processes is given using only correlation functions. This provides
a mathematical foundation for linear stationary filtering transformations of
quantum stochastic processes. It is proved that the colored quantum stationary
noise and its time-reversed version can be obtained in the second order theory
by a linear nonadapted filtering of the standard vacuum noise uniquely defined
by the canonical creation and annihilation operators on the spectrum of the
input-output pair.


title: Image compression and entanglement

abstract:
  The pixel values of an image can be casted into a real ket of a Hilbert space
using an appropriate block structured addressing. The resulting state can then
be rewritten in terms of its matrix product state representation in such a way
that quantum entanglement corresponds to classical correlations between
different coarse-grained textures. A truncation of the MPS representation is
tantamount to a compression of the original image. The resulting algorithm can
be improved adding a discrete Fourier transform preprocessing and a further
entropic lossless compression.


title: Kindergarten Quantum Mechanics

abstract:
  These lecture notes survey some joint work with Samson Abramsky as it was
presented by me at several conferences in the summer of 2005. It concerns
`doing quantum mechanics using only pictures of lines, squares, triangles and
diamonds'. This picture calculus can be seen as a very substantial extension of
Dirac's notation, and has a purely algebraic counterpart in terms of so-called
Strongly Compact Closed Categories (introduced by Abramsky and I in
quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement
quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer
to a previous set of lecture notes quant-ph/0506132. In a last section we
provide some pointers to the body of technical literature on the subject.


title: Programmable quantum channels and measurements

abstract:
  We review some partial results for two strictly related problems. The first
problem consists in finding the optimal joint unitary transformation on system
and ancilla which is the most efficient in programming any desired channel on
the system by changing the state of the ancilla. In this respect we present a
solution for dimension two for both system and ancilla. The second problem
consists in finding the optimal universal programmable detector, namely a
device that can be tuned to perform any desired measurement on a given quantum
system, by changing the state of an ancilla. With a finite dimension for the
ancilla only approximate universal programmability is possible, with minimal
dimension increasing function versus the precision of the approximation. We
show that one can achieve a dimension growing polynomially versus the
precision, and even linearly in specific cases.


title: Quantum Teleportation with a 3-Bell-state Analyzer

abstract:
  We present a novel Bell-state analyzer for time-bin qubits allowing the
detection of three out of four Bell-states with linear optics, only two
detectors and no auxiliary photons. The theoretical success rate of this scheme
is 50%. A teleportation experiment was performed to demonstrate its
functionality. We also present a teleportation experiment with a fidelity
larger than the cloning limit.


title: The distillability problem revisited

abstract:
  An important open problem in quantum information theory is the question of
the existence of NPT bound entanglement. In the past years, little progress has
been made, mainly because of the lack of mathematical tools to address the
problem. (i) In an attempt to overcome this, we show how the distillability
problem can be reformulated as a special instance of the separability problem,
for which a large number of tools and techniques are available. (ii) Building
up to this we also show how the problem can be formulated as a Schmidt number
problem. (iii) A numerical method for detecting distillability is presented and
strong evidence is given that all 1-copy undistillable Werner states are also
4-copy undistillable. (iv) The same method is used to estimate the volume of
distillable states, and the results suggest that bound entanglement is
primarily a phenomenon found in low dimensional quantum systems. (v) Finally, a
set of one parameter states is presented which we conjecture to exhibit all
forms of distillability.


title: Phase controlled light switching at low power levels

abstract:
  We report experimental observations of interference between three-photon and
one-photon excitations, and phase control of light attenuation/transmission in
a four-level system. Either constructive interference or destructive
interference can be obtained by varying the phase and/or frequency of a weak
control laser. The interference enables absorptive switching of one field by
another field at different frequencies and ultra-low light levels.


title:
Decoherence induced by a chaotic environment: A quantum walker with a
  complex coin

abstract:
  We study the differences between the process of decoherence induced by
chaotic and regular environments. For this we analyze a family of simple models
wich contain both regular and chaotic environments. In all cases the system of
interest is a "quantum walker", i.e. a quantum particle that can move on a
lattice with a finite number of sites. The walker interacts with an environment
wich has a D dimensional Hilbert space. The results we obtain suggest that
regular and chaotic environments are not distinguishable from each other in a
(short) timescale t*, wich scales with the dimensionality of the environment as
t*~log(D). Howeber, chaotic environments continue to be effective over
exponentially longer timescales while regular environments tend to reach
saturation much sooner. We present both numerical and analytical results
supporting this conclusion. The family of chaotic evolutions we consider
includes the so-called quantum multi-baker-map as a particular case.


title: Time Displaced Entanglement and Non-Linear Quantum Evolution

abstract:
  We discuss time displaced entanglement, produced by taking one member of a
Bell pair on a round trip at relativistic speeds, thus inducing a time-shift
between the pair. We show that decoherence with respect to Bell measurements on
the pair is predicted. We then study a teleportation protocol, using time
displaced entanglement as its resource, in which a time-like loop is apparently
formed. The result is non-unitary, non-linear evolution of the teleported
state.


title: Can a "Hidden Variable'' Quantum Theory Evade the "No-Cloning" Theorem?

abstract:
  If YES, then we can look forward to physical realization of superluminal
communication, as the original considerations of the ``no-cloning'' theorem
were motivated in part as an explanation of why certain schemes for
superluminal signaling cannot work.
  If NO, then it would seem that some aspects of the ``hidden'' variables must
be ``intrinsically hidden'', i.e., ``unknowable'', such that
``hidden-variable'' theories belong more to the ``idealist'' than to the
``realist'' school of thought.
  I pose this question without proposing a definite answer. I am unaware of any
commentary on this topic during these 23 years since the formulation of the
``no-cloning'' theorem, but I would be pleased to be enlightened by more
knowledgeable readers.


title: A reduction theorem for capacity of positive maps

abstract:
  We prove a reduction theorem for capacity of positive maps of finite
dimensional C*-algebras, thus reducing the computation of capacity to the case
when the image of a nonscalar projection is never a projection.


title:
Asymptotic correctability of Bell-diagonal quantum states and maximum
  tolerable bit error rates

abstract:
  The general conditions are discussed which quantum state purification
protocols have to fulfill in order to be capable of purifying Bell-diagonal
qubit-pair states, provided they consist of steps that map Bell-diagonal states
to Bell-diagonal states and they finally apply a suitably chosen
Calderbank-Shor-Steane code to the outcome of such steps. As a main result a
necessary and a sufficient condition on asymptotic correctability are
presented, which relate this problem to the magnitude of a characteristic
exponent governing the relation between bit and phase errors under the
purification steps. These conditions allow a straightforward determination of
maximum tolerable bit error rates of quantum key distribution protocols whose
security analysis can be reduced to the purification of Bell-diagonal states.


title: Entangled Quantum States Generated by Shor's Factoring Algorithm

abstract:
  The intermediate quantum states of multiple qubits, generated during the
operation of Shor's factoring algorithm are analyzed. Their entanglement is
evaluated using the Groverian measure. It is found that the entanglement is
generated during the pre-processing stage of the algorithm and remains nearly
constant during the quantum Fourier transform stage. The entanglement is found
to be correlated with the speedup achieved by the quantum algorithm compared to
classical algorithms.


title:
Radiation reaction on charged particles in three-dimensional motion in
  classical and quantum electrodynamics

abstract:
  We extend our previous work (see arXiv:quant-ph/0501026), which compared the
predictions of quantum electrodynamics concerning radiation reaction with those
of the Abraham-Lorentz-Dirac theory for a charged particle in linear motion.
Specifically, we calculate the predictions for the change in position of a
charged scalar particle, moving in three-dimensional space, due to the effect
of radiation reaction in the one-photon-emission process in quantum
electrodynamics. The scalar particle is assumed to be accelerated for a finite
period of time by a three-dimensional electromagnetic potential dependent only
on one of the spacetime coordinates. We perform this calculation in the
$\hbar\to 0$ limit and show that the change in position agrees with that
obtained in classical electrodynamics with the Lorentz-Dirac force treated as a
perturbation. We also show for a time-dependent but space-independent
electromagnetic potential that the forward-scattering amplitude at order $e^2$
does not contribute to the position change in the $\hbar \to 0$ limit after the
mass renormalization is taken into account.


title: Concentration for unknown atomic entangled states via cavity decay

abstract:
  We present a physical scheme for entanglement concentration of unknown atomic
entangled states via cavity decay. In the scheme, the atomic state is used as
stationary qubit and photonic state as flying qubit, and a close maximally
entangled state can be obtained from pairs of partially entangled states
probabilistically.


title:
Almost Optimal Solution of Initial-Value Problems by Randomized and
  Quantum Algorithms

abstract:
  We establish essentially optimal bounds on the complexity of initial-value
problems in the randomized and quantum settings. For this purpose we define a
sequence of new algorithms whose error/cost properties improve from step to
step. These algorithms yield new upper complexity bounds, which differ from
known lower bounds by only an arbitrarily small positive parameter in the
exponent, and a logarithmic factor. In both the randomized and quantum
settings, initial-value problems turn out to be essentially as difficult as
scalar integration.


title: Quantum Walk with a time-dependent coin

abstract:
  We introduce quantum walks with a time-dependent coin, and show how they
include, as a particular case, the generalized quantum walk recently studied by
Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits
interesting dynamical localization and quasiperiodic dynamics. Our proposal
allows for a much easier implementation of this particular rich dynamics than
the original one. Moreover, it allows for an additional control on the walk,
which can be used to compensate for phases appearing due to external
interactions. To illustrate its feasibility, we discuss an example using an
optical cavity. We also derive an approximated solution in the continuous limit
(long--wavelength approximation) which provides physical insight about the
process.


title: First principles quantum Monte Carlo

abstract:
  Present quantum Monte Carlo codes use statistical techniques adapted to find
the amplitude of a quantum system or the associated eigenvalues. Thus, they do
not use a true physical random source. It is demonstrated that, in fact,
quantum probability admits a description based on a specific class of random
process at least for the single particle case. Then a first principle Monte
Carlo code that exactly simulates quantum dynamics can be constructed. The
subtle question concerning how to map random choices in amplitude interferences
is explained. Possible advantages of this code in simulating single hit
experiments are discussed.


title:
Time-reversal formalism applied to maximal bipartite entanglement:
  Theoretical and experimental exploration

abstract:
  Within the context of quantum teleportation, a proposed intuitive model to
explain bipartite entanglement describes the scheme as being the same qubit of
information evolving along and against the flow of time of an external
observer. We investigate the physicality of such a model by applying the
time-reversal of the Schrodinger equation in the teleportation context. To do
so, we first lay down the theory of time-reversal applied to the circuit model
and then show that the outcome of a teleportation-like circuit is consistent
with the usual tensor product treatment, thus independent of the physical
quantum system used to encode the information. Finally, we demonstrate a proof
of principle experiment on a liquid state NMR quantum information processor.
The experimental results are consistent with the interpretation that
information can be seen as flowing backward in time through entanglement.


title:
Berry's phases and topological properties in the Born-Oppenheimer
  approximation

abstract:
  The level crossing problem is neatly formulated by the second quantized
formulation, which exhibits a hidden local gauge symmetry. The analysis of
geometric phases is reduced to a simple diagonalization of the Hamiltonian. If
one diagonalizes the geometric terms in the infinitesimal neighborhood of level
crossing, the geometric phases become trivial (and thus no monopole
singularity) for arbitrarily large but finite time interval $T$. The
topological proof of the Longuet-Higgins' phase-change rule, for example, thus
fails in the practical Born-Oppenheimer approximation where $T$ is identified
with the period of the slower system. The crucial difference between the
Aharonov-Bohm phase and the geometric phase is explained. It is also noted that
the gauge symmetries involved in the adiabatic and non-adiabatic geometric
phases are quite different.


title:
Constant communication complexity protocols for multiparty accumulative
  boolean functions

abstract:
  Generalizing a boolean function from Cleve and Buhrman \cite{cb:sqec}, we
consider the class of {\it accumulative boolean functions} of the form
$f_B(X_1,X_2,..., X_m)=\bigoplus_{i=1}^n t_B(x_i^1x_i^2... x_i^m)$, where
$X_j=(x^j_1,x^j_2,..., x^j_n), 1\leq j\leq m$ and $t_B(x_i^1x_i^2... x_i^m)=1$
for input $m$-tuples $x_i^1x_i^2...x_i^m\in B\subseteq A\subseteq \{0,1\}^n$,
and 0, if $x_i^1x_i^2...x_i^m\in A\setminus B$. Here the set $A$ is the input
{\it promise} set for function $f_B$. The input vectors $X_j, 1\leq j\leq m$
are given to the $m\geq 3$ parties respectively, who communicate cbits in a
distributed environment so that one of them (say Alice) comes up with the value
of the function. We algebraically characterize entanglement assisted LOCC
protocols requiring only $m-1$ cbits of communication for such multipartite
boolean functions $f_B$, for certain sets $B\subseteq \{0,1\}^n$, for $m\geq 3$
parties under appropriate uniform parity promise restrictions on input
$m$-tuples $x_i^1x_i^2...x_i^m, 1\leq i\leq n$. We also show that these
functions can be computed using $2m-3$ cbits in a purely classical
deterministic setup. In contrast, for certain $m$-party accumulative boolean
functions ($m\geq 2$), we characterize promise sets of mixed parity for input
$m$-tuples so that $m-1$ cbits of communication suffice in computing the
functions in the absence of any a priori quantum entanglement. We compactly
represent all these protocols and the corresponding input promise restrictions
using uniform group theoretic and hamming distance characterizations.


title: Robust Entanglement through Macroscopic Quantum Jumps

abstract:
  We propose an entanglement generation scheme that requires neither the
coherent evolution of a quantum system nor the detection of single photons.
Instead, the desired state is heralded by a {\em macroscopic} quantum jump.
Macroscopic quantum jumps manifest themselves as a random telegraph signal with
long intervals of intense fluorescence (light periods) interrupted by the
complete absence of photons (dark periods). Here we show that a system of two
atoms trapped inside an optical cavity can be designed such that a dark period
prepares the atoms in a maximally entangled ground state. Achieving fidelities
above 0.9 is possible even when the single-atom cooperativity parameter C is as
low as 10 and when using a photon detector with an efficiency as low as eta =
0.2.


title: Bipartite and Multipartite Entanglement of Gaussian States

abstract:
  In this chapter we review the characterization of entanglement in Gaussian
states of continuous variable systems. For two-mode Gaussian states, we discuss
how their bipartite entanglement can be accurately quantified in terms of the
global and local amounts of mixedness, and efficiently estimated by direct
measurements of the associated purities. For multimode Gaussian states endowed
with local symmetry with respect to a given bipartition, we show how the
multimode block entanglement can be completely and reversibly localized onto a
single pair of modes by local, unitary operations. We then analyze the
distribution of entanglement among multiple parties in multimode Gaussian
states. We introduce the continuous-variable tangle to quantify entanglement
sharing in Gaussian states and we prove that it satisfies the
Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure,
symmetric three-mode Gaussian states, at variance with their discrete-variable
counterparts, allow a promiscuous sharing of quantum correlations, exhibiting
both maximum tripartite residual entanglement and maximum couplewise
entanglement between any pair of modes. Finally, we investigate the connection
between multipartite entanglement and the optimal fidelity in a
continuous-variable quantum teleportation network. We show how the fidelity can
be maximized in terms of the best preparation of the shared entangled resources
and, viceversa, that this optimal fidelity provides a clearcut operational
interpretation of several measures of bipartite and multipartite entanglement,
including the entanglement of formation, the localizable entanglement, and the
continuous-variable tangle.

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


title:
Generating continuous variable quantum codewords in the near-field
  atomic lithography

abstract:
  Recently, D. Gottesman et al. [Phys. Rev. A 64, 012310 (2001)] showed how to
encode a qubit into a continuous variable quantum system. This encoding was
realized by using non-normalizable quantum codewords, which therefore can only
be approximated in any real physical setup. Here we show how a neutral atom,
falling through an optical cavity and interacting with a single mode of the
intracavity electromagnetic field, can be used to safely encode a qubit into
its external degrees of freedom. In fact, the localization induced by a
homodyne detection of the cavity field is able to project the near-field atomic
motional state into an approximate quantum codeword. The performance of this
encoding process is then analyzed by evaluating the intrinsic errors induced in
the recovery process by the approximated form of the generated codeword.


title:
Thermal quantum field theory and the Casimir interaction between
  dielectrics

abstract:
  The Casimir and van der Waals interaction between two dissimilar thick
dielectric plates is reconsidered on the basis of thermal quantum field theory
in Matsubara formulation. We briefly review two main derivations of the
Lifshitz formula in the framework of thermal quantum field theory without use
of the fluctuation-dissipation theorem. A set of special conditions is
formulated under which these derivations remain valid in the presence of
dissipation. The low-temperature behavior of the Casimir and van der Waals
interactions between dissimilar dielectrics is found analytically from the
Lifshitz theory for both an idealized model of dilute dielectrics and for real
dielectrics with finite static dielectric permittivities. The free energy,
pressure and entropy of the Casimir and van der Waals interactions at low
temperatures demonstrate the same universal dependence on the temperature as
was previously discovered for ideal metals. The entropy vanishes when
temperature goes to zero proving the validity of the Nernst heat theorem. This
solves the long-standing problem on the consistency of the Lifshitz theory with
thermodynamics in the case of dielectric plates. The obtained asymptotic
expressions are compared with numerical computations for both dissimilar and
similar real dielectrics and found to be in excellent agreement. The role of
the zero-frequency term in Matsubara sum is investigated in the case of
dielectric plates. It is shown that the inclusion of conductivity in the model
of dielectric response leads to the violation of the Nernst heat theorem. The
applications of this result to the topical problems of noncontact atomic
friction and the Casimir interaction between real metals are discussed.


title:
Measurement-Induced Entanglement for Excitation Stored in Remote Atomic
  Ensembles

abstract:
  A critical requirement for diverse applications in Quantum Information
Science is the capability to disseminate quantum resources over complex quantum
networks. For example, the coherent distribution of entangled quantum states
together with quantum memory to store these states can enable scalable
architectures for quantum computation, communication, and metrology. As a
significant step toward such possibilities, here we report observations of
entanglement between two atomic ensembles located in distinct apparatuses on
different tables. Quantum interference in the detection of a photon emitted by
one of the samples projects the otherwise independent ensembles into an
entangled state with one joint excitation stored remotely in 10^5 atoms at each
site. After a programmable delay, we confirm entanglement by mapping the state
of the atoms to optical fields and by measuring mutual coherences and photon
statistics for these fields. We thereby determine a quantitative lower bound
for the entanglement of the joint state of the ensembles. Our observations
provide a new capability for the distribution and storage of entangled quantum
states, including for scalable quantum communication networks .


title:
Fidelity optimization for holonomic quantum gates in dissipative
  environments

abstract:
  We analyze the performance of holonomic quantum gates in semi-conductor
quantum dots, driven by ultrafast lasers, under the effect of a dissipative
environment. In agreement with the standard practice, the environment is
modeled as a thermal bath of oscillators linearly coupled with the excitonic
states of the quantum dot. Standard techniques of quantum dissipation make the
problem amenable to a numerical treatment and allow to determine the fidelity
(the common gate-performance estimator), as a function of all the relevant
physical parameters. As a consequence of our analysis, we show that, by varying
in a suitable way the controllable parameters, the disturbance of the
environment can be (approximately) suppressed, and the performance of the gate
optimized--provided that the thermal bath is purely superhomic. We conclude by
showing that such an optimization it is impossible for ohmic environments.


title: Generation of a coherent superposition state on demand

abstract:
  We propose an experimentally feasible scheme to generate a superposition of
travelling field coherent states using extremely small Kerr effect and an
ancilla which could be a single photon or two entangled twin photons. The
scheme contains ingredients which are all within the current state of the art
and is robust against the main sources of errors which can be identified in our
setups.


title:
Bound-state eigenenergy outside and inside the continuum for unstable
  multilevel systems

abstract:
  The eigenvalue problem for the dressed bound-state of unstable multilevel
systems is examined both outside and inside the continuum, based on the N-level
Friedrichs model which describes the couplings between the discrete levels and
the continuous spectrum. It is shown that a bound-state eigenenergy always
exists below each of the discrete levels that lie outside the continuum.
Furthermore, by strengthening the couplings gradually, the eigenenergy
corresponding to each of the discrete levels inside the continuum finally
emerges. On the other hand, the absence of the eigenenergy inside the continuum
is proved in weak but finite coupling regimes, provided that each of the form
factors that determine the transition between some definite level and the
continuum does not vanish at that energy level. An application to the
spontaneous emission process for the hydrogen atom interacting with the
electromagnetic field is demonstrated.


title:
On a heuristic point of view concerning the motion of matter. From
  random metric to Schroedinger equation

abstract:
  The motion of a particle is studied in a random space-time. It is assumed
that the velocity is small enough for the non-relativistic approximation to be
valid. The randomness of the metric induces a diffusion in coordinate space.
Hence it is shown that the evolution of the probability density is given by
Schroedinger equation.


title:
Complex Energies and Beginnings of Time Suggest a Theory of Scattering
  and Decay

abstract:
  Many useful concepts for a quantum theory of scattering and decay (like
Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially
decaying Gamow vectors, causality) are not well defined in the mathematical
frame set by the conventional (Hilbert space) axioms of quantum mechanics.
Using the Lippmann-Schwinger equations as the takeoff point and aiming for a
theory that unites resonances and decay, we conjecture a new axiom for quantum
mechanics that distinguishes mathematically between prepared states and
detected observables. Suggested by the two signs $\pm i\epsilon$ of the
Lippmann-Schwinger equations, this axiom replaces the one Hilbert space of
conventional quantum mechanics by two Hardy spaces. The new Hardy space theory
automatically provides Gamow kets with exponential time evolution derived from
the complex poles of the $S$-matrix. It solves the causality problem since it
results in a semigroup evolution. But this semigroup brings into quantum
physics a new concept of the semigroup time $t=0$, a beginning of time. Its
interpretation and observations are discussed in the last section.


title: Theory of Single Photon Control from a Two Level System Source

abstract:
  Generation of a single photon or a pair of photons from a single emitter is
important for quantum information applications. Using the generating function
formalism we investigate the theory of a few photons on demand for the square
laser pulse and the rapid adiabatic following method. Exact theory and
numerical solutions are used to design control fields for a two level emitter,
which yield an optimal single or two photon source, under the constrains of
finite laser field strength and finite interaction time. Comparison to
experiments of Brunel et al, shows that the experiments were made close to
optimal conditions.


title:
Quantum key distribution at telecom wavelengths with noise-free
  detectors

abstract:
  The length of a secure link over which a quantum key can be distributed
depends on the efficiency and dark-count rate of the detectors used at the
receiver. We report on the first demonstration of quantum key distribution
using transition-edge sensors with high efficiency and negligible dark-count
rates. Using two methods of synchronization, a bright optical pulse scheme and
an electrical signal scheme, we have successfully distributed key material at
1,550 nm over 50 km of optical fiber. We discuss how use of these detectors in
a quantum key distribution system can result in dramatic increases in range and
performance.


title:
Type-II Optical Parametric Oscillator : a versatile source of quantum
  correlations and entanglement

abstract:
  Type-II Optical Parametric Oscillators are efficient sources of quadrature
squeezed or polarization squeezed light, intensity correlated beams, and
entangled light. We review here the different levels of quantum correlations
and entanglement that are reached in this device, and present some
applications.


title:
Entanglement of mixed macroscopic superpositions: an entangling-power
  study

abstract:
  We investigate entanglement properties of a recently introduced class of
macroscopic quantum superpositions in two-mode mixed states. One of the tools
we use in order to infer the entanglement in this non-Gaussian class of states
is the power to entangle a qubit system. Our study reveals features which are
hidden in a standard approach to entanglement investigation based on the
uncertainty principle of the quadrature variables. We briefly describe the
experimental setup corresponding to our theoretical scenario and a suitable
modification of the protocol which makes our proposal realizable within the
current experimental capabilities.


title:
The stationary phase condition applicability to the study of tunnel
  effect

abstract:
  Some recent theoretical studies have tended to employ analytically-continuous
{\em gaussian}, or infinite-bandwidth step pulses to examine tunneling process.
The stationary phase method is often employed to this aim. However, {\em
gaussian} functions do not have a well-defined front, such that their speed of
propagation becomes ambiguous. Also, infinite bandwidth signals cannot
propagate through any real physical medium (whose transfer function is
therefore finite) without pulse distortion, which also leads to ambiguities in
determining propagation velocity during the tunneling process. In this
manuscript, we appoint some incompatibilities with the application of the
method of stationary phase in deriving tunneling times which, eventually, can
ruin the {\em superluminal} interpretation of transition times.


title: Implementation of Grover's Quantum Search Algorithm in a Scalable System

abstract:
  We report the implementation of Grover's quantum search algorithm in the
scalable system of trapped atomic ion quantum bits. Any one of four possible
states of a two-qubit memory is marked, and following a single query of the
search space, the marked element is successfully recovered with an average
probability of 60(2)%. This exceeds the performance of any possible classical
search algorithm, which can only succeed with a maximum average probability of
50%.


title:
Quantum key distribution based on arbitrarily-weak distillable entangled
  states

abstract:
  States with private correlations but little or no distillable entanglement
were recently reported. Here, we consider the secure distribution of such
states, i.e., the situation when an adversary gives two parties such states and
they have to verify privacy. We present a protocol which enables the parties to
extract from such untrusted states an arbitrarily long and secure key, even
though the amount of distillable entanglement of the untrusted states can be
arbitrarily small.


title:
Geometric Phase Transition: direct measurement of a mathematical
  abstraction

abstract:
  By viewing entanglement as a state function, a new kind of phase transition
takes place: the geometric phase transition. This phenomenon occurs due to
singularities in the shape of the entangled states set. It is shown how this
result can be carried to provide a better understanding of the geometry of
entanglement. Surprisingly, this study can be done experimentally, what allows
to determine the shape of different entangled states sets, a purely
mathematical definition, in real experiments.


title: Uncertainty Principle and the Standard Quantum Limits

abstract:
  The role of the Uncertainty Principle is examined through the examples of
squeezing, information capacity, and position monitoring. It is suggested that
more attention should be directed to conceptual considerations in quantum
information science and technology.


title:
Exact Diagonalisation of The XY-Hamiltonian of Open Linear Chains with
  Periodic Coupling Constants and Its Application to Dynamics of
  One-Dimensional Spin Systems

abstract:
  A new method of diagonalisation of the XY-Hamiltonian of inhomogeneous open
linear chains with periodic (in space) changing Larmor frequencies and coupling
constants is developed. As an example of application, multiple quantum dynamics
of an inhomogeneous chain consisting of 1001 spins is investigated. Intensities
of multiple quantum coherences are calculated for arbitrary inhomogeneous
chains in the approximation of the next nearest interactions.
  {\it Key words:} linear spin chain, nearest--neighbour approximation,
three--diagonal matrices, diagonalisation, fermions, multiple--quantum NMR,
multiple--quantum coherence, intensities of multiple--quantum coherences.
  {\it PACS numbers:} 05.30.-d; 76.20.+q


title: Ground State Instabilities and Entanglement in the Detuned Dicke Model

abstract:
  Ground state instabilities of the spin-boson model is studied in this work.
The existence of sequential ground state instabilities is shown analytically
for arbitrary detuning in the two-spin system. In this model, extra
discontinuities of concurrence(entanglement measure) are found in the finite
system, which do not appear in the on-resonant model. The above results remain
intact by including extra boson modes. Moreover, by including extra modes, it
is found that ground state entanglement can be obtained and enhanced even in
the weak coupling regime.


title: Locality in Nonsequential Quantum Operations

abstract:
  We give an example of fulfillment of the condition of locality--no
information transfer between certain subsystems--in a tripartite quantum system
whose dynamics can not be decomposed (non-sequential dynamics of the system).
The three subsystems ($A$, $B$ and $C$) are designed such that $C$ interacts
simultaneously with both $A$ and $B$, while there is not any interaction
between $A$ and $B$. On this basis, we emphasize validity of the condition of
locality in a realistic physical situation.


title: Entropic characteristics of subsets of states

abstract:
  This paper is devoted to systematic study of properties of the quantum
entropy and of the Holevo capacity considered as a function of a set of quantum
states.
  The properties of restriction of the quantum entropy to arbitrary set of
states are discussed. For some types of sets necessary and sufficient
conditions of boundedness and of continuity of restriction of the quantum
entropy as well as necessary and sufficient conditions of existence of the
Gibbs state are obtained.
  The Holevo capacity of an arbitrary set of states and its general properties
as a function of a set are considered. The notion of the optimal average state
of an arbitrary set of states with finite Holevo capacity is introduced. The
condition of existence of optimal measure for a set of states is obtained.
  The general results concerning the quantum entropy and the Holevo capacity
are illustrated by considering the several examples of sets of states.


title: Continuous variable remote state preparation

abstract:
  We extend exact deterministic remote state preparation (RSP) with minimal
classical communication to quantum systems of continuous variables. We show
that, in principle, it is possible to remotely prepare states of an ensemble
that is parameterized by infinitely many real numbers, i.e., by a real
function, while the classical communication cost is one real number only. We
demonstrate continuous variable RSP in three examples using (i) quadrature
measurement and phase space displacement operations, (ii) measurement of the
optical phase and unitaries shifting the same, and (iii) photon counting and
photon number shift.


title:
Weak and strong coupling regimes, vacuum Rabi splitting and nonstandard
  resonances

abstract:
  For two discrete-level quantum systems in interaction, we follow the
displacement in the complex plane of the eigen-energies of the compound system
when the spectrum of one of the two systems becomes continuous. These new
points are usually called resonances. This allows us to define and to calculate
a critical value of the coupling constant which separates two well-known
coupling regimes. We also give an example of these resonances for the hydrogen
atom coupled to the continuum of the states of the transverse electromagnetic
field in the vacuum. We justify that some resonances be neglected.


title: Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities

abstract:
  Quantum theory imposes a strict limit on the strength of non-local
correlations. It only allows for a violation of the CHSH inequality up to the
value 2 sqrt(2), known as Tsirelson's bound. In this note, we consider
generalized CHSH inequalities based on many measurement settings with two
possible measurement outcomes each. We demonstrate how to prove Tsirelson
bounds for any such generalized CHSH inequality using semidefinite programming.
As an example, we show that for any shared entangled state and observables
X_1,...,X_n and Y_1,...,Y_n with eigenvalues +/- 1 we have |<X_1 Y_1> + <X_2
Y_1> + <X_2 Y_2> + <X_3 Y_2> + ... + <X_n Y_n> - <X_1 Y_n>| <= 2 n
cos(pi/(2n)). It is well known that there exist observables such that equality
can be achieved. However, we show that these are indeed optimal. Our approach
can easily be generalized to other inequalities for such observables.


title: Optimal entanglement witnesses for continuous-variable systems

abstract:
  This paper is concerned with all tests for continuous-variable entanglement
that arise from linear combinations of second moments or variances of canonical
coordinates, as they are commonly used in experiments to detect entanglement.
All such tests for bi-partite and multi-partite entanglement correspond to
hyperplanes in the set of second moments. It is shown that all optimal tests,
those that are most robust against imperfections with respect to some figure of
merit for a given state, can be constructed from solutions to semi-definite
optimization problems. Moreover, we show that for each such test, referred to
as entanglement witness based on second moments, there is a one-to-one
correspondence between the witness and a stronger product criterion, which
amounts to a non-linear witness, based on the same measurements. This
generalizes the known product criteria. The presented tests are all applicable
also to non-Gaussian states. To provide a service to the community, we present
the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have
been made publicly available.


title: Entanglement activation and the robustness of quantum correlations

abstract:
  We show that the usefulness of a state as an activator in teleportation
protocols is equivalent to the robustness of its entanglement to noise. The
robustness of entanglement of a bi-partite state is linked to the maximum
increase in the the fidelity of teleportation of any other state when the
former is used as an extra resource. On the one hand, this connection gives an
operational meaning to the robustness of entanglement. On the other hand, it
shows that the activation capability - which has a central role as an
operational way of quantifying bound entangled states - can be estimated
experimentally by measuring entanglement witnesses.


title:
Monomiality principle, Sheffer-type polynomials and the normal ordering
  problem

abstract:
  We solve the boson normal ordering problem for $(q(a^\dag)a+v(a^\dag))^n$
with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and
$a^\dag$ are boson annihilation and creation operators, satisfying
$[a,a^\dag]=1$. This consequently provides the solution for the exponential
$e^{\lambda(q(a^\dag)a+v(a^\dag))}$ generalizing the shift operator. In the
course of these considerations we define and explore the monomiality principle
and find its representations. We exploit the properties of Sheffer-type
polynomials which constitute the inherent structure of this problem. In the end
we give some examples illustrating the utility of the method and point out the
relation to combinatorial structures.


title: Exponential Operators, Dobinski Relations and Summability

abstract:
  We investigate properties of exponential operators preserving the particle
number using combinatorial methods developed in order to solve the boson normal
ordering problem. In particular, we apply generalized Dobinski relations and
methods of multivariate Bell polynomials which enable us to understand the
meaning of perturbation-like expansions of exponential operators. Such
expansions, obtained as formal power series, are everywhere divergent but the
Pade summation method is shown to give results which very well agree with exact
solutions got for simplified quantum models of the one mode bosonic systems.


title:
Transition from discrete to continuous time of arrival distribution for
  a quantum particle

abstract:
  We show that the Kijowski distribution for time of arrivals in the entire
real line is the limiting distribution of the time of arrival distribution in a
confining box as its length increases to infinity. The dynamics of the confined
time of arrival eigenfunctions is also numerically investigated and
demonstrated that the eigenfunctions evolve to have point supports at the
arrival point at their respective eigenvalues in the limit of arbitrarilly
large confining lengths, giving insight into the ideal physical content of the
Kijowsky distribution.


title: Combinatorial Solutions to Normal Ordering of Bosons

abstract:
  We present a combinatorial method of constructing solutions to the normal
ordering of boson operators. Generalizations of standard combinatorial notions
- the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead
to calculational tools which allow to find explicitly normally ordered forms
for a large class of operator functions.


title: Universal Uncertainty Principle in the Measurement Operator Formalism

abstract:
  Heisenberg's uncertainty principle has been understood to set a limitation on
measurements; however, the long-standing mathematical formulation established
by Heisenberg, Kennard, and Robertson does not allow such an interpretation.
Recently, a new relation was found to give a universally valid relation between
noise and disturbance in general quantum measurements, and it has become clear
that the new relation plays a role of the first principle to derive various
quantum limits on measurement and information processing in a unified
treatment. This paper examines the above development on the noise-disturbance
uncertainty principle in the model-independent approach based on the
measurement operator formalism, which is widely accepted to describe a class of
generalized measurements in the field of quantum information. We obtain
explicit formulas for the noise and disturbance of measurements given by the
measurement operators, and show that projective measurements do not satisfy the
Heisenberg-type noise-disturbance relation that is typical in the gamma-ray
microscope thought experiments. We also show that the disturbance on a Pauli
operator of a projective measurement of another Pauli operator constantly
equals the square root of 2, and examine how this measurement violates the
Heisenberg-type relation but satisfies the new noise-disturbance relation.


title: Quantum Complexity Bounds for Independent Set Problems

abstract:
  We present quantum complexity lower and upper bounds for independent set
problems in graphs. In particular, we give quantum algorithms for computing a
maximal and a maximum independent set in a graph. We present applications of
these algorithms for some graph problems. Our results improve the best
classical complexity bounds for the corresponding problems.


title: Random Lindblad equations from complex environments

abstract:
  In this paper we demonstrate that Lindblad equations characterized by a
random rate variable arise after tracing out a complex structured reservoir.
Our results follows from a generalization of the Born-Markov approximation,
which relies in the possibility of splitting the complex environment in a
direct sum of sub-reservoirs, each one being able to induce by itself a
Markovian system evolution. Strong non-Markovian effects, which microscopically
originate from the entanglement with the different sub-reservoirs, characterize
the average system decay dynamics. As an example, we study the anomalous
irreversible behavior of a quantum tunneling system described in an effective
two level approximation. Stretched exponential and power law decay behaviors
arise from the interplay between the dissipative and unitary hopping dynamics.


title:
Optimal Pointers for Joint Measurement of sigma-x and sigma-z via
  Homodyne Detection

abstract:
  We study a model of a two-level system (i.e. a qubit) in interaction with the
electromagnetic field. By means of homodyne detection, one field-quadrature is
observed continuously in time. Due to the interaction, information about the
initial state of the qubit is transferred into the field, thus influencing the
homodyne measurement results. We construct random variables (pointers) on the
probability space of homodyne measurement outcomes having distributions close
to the initial distributions of sigma-x and sigma-z. Using variational
calculus, we find the pointers that are optimal. These optimal pointers are
very close to hitting the bound imposed by Heisenberg's uncertainty relation on
joint measurement of two non-commuting observables. We close the paper by
giving the probability densities of the pointers.


title:
Four-dimensional Quantum Key Distribution using Position-Momentum and
  Polarization Correlations

abstract:
  We demonstrate experimentally that it is possible to prepare and detect
photon pairs created by spontaneous parametric down-conversion which exhibit
simultaneous position-momentum and polarization correlations that are adequate
to implement a four-dimensional key distribution protocol.


title:
Quantum key distribution with higher-order alphabets using
  spatially-encoded qudits

abstract:
  We propose and demonstrate a quantum key distribution scheme in higher-order
$d$-dimensional alphabets using spatial degrees of freedom of photons. Our
implementation allows for the transmission of 4.56 bits per sifted photon,
while providing improved security: an intercept-resend attack on all photons
would induce an error rate of 0.47. Using our system, it should be possible to
send more than a byte of information per sifted photon.


title: Expanded Quantum Cryptographic Entangling Probe

abstract:
  The paper [Howard E. Brandt, "Quantum Cryptographic Entangling Probe," Phys.
Rev. A 71, 042312 (2005)] is generalized to include the full range of error
rates for the projectively measured quantum cryptographic entangling probe.


title:
Reconciling Spacetime and the Quantum: Relational Blockworld and the
  Quantum Liar Paradox

abstract:
  The Relational Blockworld (RBW) interpretation of non-relativistic quantum
mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a
relational, non-separable blockworld whereby spatial distance is only defined
between interacting trans-temporal objects. RBW is shown to provide a novel
statistical interpretation of the wavefunction that deflates the measurement
problem, as well as a geometric account of quantum entanglement and
non-separability that satisfies locality per special relativity and is free of
interpretative mystery. We present RBW's acausal and adynamical resolution of
the so-called "quantum liar paradox," an experimental set-up alleged to be
problematic for a spacetime conception of reality, and conclude by speculating
on RBW's implications for quantum gravity.


title: A note on the power of quantum fingerprinting

abstract:
  In this short note, we improve and extend Yao's paper "On the power of
quantum fingerprinting" about simulating a classical public coin simultaneous
message protocol by a quantum simultaneous message protocol with no shared
resource.


title:
Generation of Werner states via collective decay of coherently driven
  atoms

abstract:
  We show deterministic generation of Werner states as a steady state of the
collective decay dynamics of a pair of neutral atom coupled to a leaky cavity
and strong coherent drive. We also show how the scheme can be extended to
generate $2N$-particle analogue of the bipartite Werner states.


title: Quantum dense coding scheme via cavity decay

abstract:
  We investigate a secure scheme for implementing quantum dense coding via
cavity decay and liner optics devices. Our scheme combines two distinct
advantages: atomic qubit sevres as stationary bit and photonic qubit as flying
bit, thus it is suitable for long distant quantum communication.


title: From Bell's Theorem to Secure Quantum Key Distribution

abstract:
  Any Quantum Key Distribution (QKD) protocol consists first of sequences of
measurements that produce some correlation between classical data. We show that
these correlation data must violate some Bell inequality in order to contain
distillable secrecy, if not they could be produced by quantum measurements
performed on a separable state of larger dimension. We introduce a new QKD
protocol and prove its security against any individual attack by an adversary
only limited by the no-signaling condition.