1,808 research outputs found
Entropy inequalities and Bell inequalities for two-qubit systems
Sufficient conditions for (the non-violation of) the Bell-CHSH inequalities
in a mixed state of a two-qubit system are: 1) The linear entropy of the state
is not smaller than 0.5, 2) The sum of the conditional linear entropies is
non-negative, 3) The von Neumann entropy is not smaller than 0.833, 4) The sum
of the conditional von Neumann entropies is not smaller than 0.280.Comment: Errors corrected. See L. Jakobcyk, quant-ph/040908
Containing epidemic outbreaks by message-passing techniques
The problem of targeted network immunization can be defined as the one of
finding a subset of nodes in a network to immunize or vaccinate in order to
minimize a tradeoff between the cost of vaccination and the final (stationary)
expected infection under a given epidemic model. Although computing the
expected infection is a hard computational problem, simple and efficient
mean-field approximations have been put forward in the literature in recent
years. The optimization problem can be recast into a constrained one in which
the constraints enforce local mean-field equations describing the average
stationary state of the epidemic process. For a wide class of epidemic models,
including the susceptible-infected-removed and the
susceptible-infected-susceptible models, we define a message-passing approach
to network immunization that allows us to study the statistical properties of
epidemic outbreaks in the presence of immunized nodes as well as to find
(nearly) optimal immunization sets for a given choice of parameters and costs.
The algorithm scales linearly with the size of the graph and it can be made
efficient even on large networks. We compare its performance with topologically
based heuristics, greedy methods, and simulated annealing
Improving teleportation of continuous variables by local operations
We study a continuous-variable (CV) teleportation protocol based on a shared
entangled state produced by the quantum-nondemolition (QND) interaction of two
vacuum states. The scheme utilizes the QND interaction or an unbalanced beam
splitter in the Bell measurement. It is shown that in the non-unity gain regime
the signal transfer coefficient can be enhanced while the conditional variance
product remains preserved by applying appropriate local squeezing operation on
sender's part of the shared entangled state. In the unity gain regime it is
demonstrated that the fidelity of teleportation can be increased with the help
of the local squeezing operations on parts of the shared entangled state that
convert effectively our scheme to the standard CV teleportation scheme.
Further, it is proved analytically that such a choice of the local symplectic
operations minimizes the noise by which the mean number of photons in the input
state is increased during the teleportation. Finally, our analysis reveals that
the local symplectic operation on sender's side can be integrated into the Bell
measurement if the interaction constant of the interaction in the Bell
measurement can be adjusted properly.Comment: 10 pages, 1 figure, discussion of the non-unity gain teleportation is
adde
Optimizing spread dynamics on graphs by message passing
Cascade processes are responsible for many important phenomena in natural and
social sciences. Simple models of irreversible dynamics on graphs, in which
nodes activate depending on the state of their neighbors, have been
successfully applied to describe cascades in a large variety of contexts. Over
the last decades, many efforts have been devoted to understand the typical
behaviour of the cascades arising from initial conditions extracted at random
from some given ensemble. However, the problem of optimizing the trajectory of
the system, i.e. of identifying appropriate initial conditions to maximize (or
minimize) the final number of active nodes, is still considered to be
practically intractable, with the only exception of models that satisfy a sort
of diminishing returns property called submodularity. Submodular models can be
approximately solved by means of greedy strategies, but by definition they lack
cooperative characteristics which are fundamental in many real systems. Here we
introduce an efficient algorithm based on statistical physics for the
optimization of trajectories in cascade processes on graphs. We show that for a
wide class of irreversible dynamics, even in the absence of submodularity, the
spread optimization problem can be solved efficiently on large networks.
Analytic and algorithmic results on random graphs are complemented by the
solution of the spread maximization problem on a real-world network (the
Epinions consumer reviews network).Comment: Replacement for "The Spread Optimization Problem
Broadband teleportation
Quantum teleportation of an unknown broadband electromagnetic field is
investigated. The continuous-variable teleportation protocol by Braunstein and
Kimble [Phys. Rev. Lett. {\bf 80}, 869 (1998)] for teleporting the quantum
state of a single mode of the electromagnetic field is generalized for the case
of a multimode field with finite bandwith. We discuss criteria for
continuous-variable teleportation with various sets of input states and apply
them to the teleportation of broadband fields. We first consider as a set of
input fields (from which an independent state preparer draws the inputs to be
teleported) arbitrary pure Gaussian states with unknown coherent amplitude
(squeezed or coherent states). This set of input states, further restricted to
an alphabet of coherent states, was used in the experiment by Furusawa {\it et
al.} [Science {\bf 282}, 706 (1998)]. It requires unit-gain teleportation for
optimizing the teleportation fidelity. In our broadband scheme, the excess
noise added through unit-gain teleportation due to the finite degree of the
squeezed-state entanglement is just twice the (entanglement) source's squeezing
spectrum for its ``quiet quadrature.'' The teleportation of one half of an
entangled state (two-mode squeezed vacuum state), i.e., ``entanglement
swapping,'' and its verification are optimized under a certain nonunit gain
condition. We will also give a broadband description of this
continuous-variable entanglement swapping based on the single-mode scheme by
van Loock and Braunstein [Phys. Rev. A {\bf 61}, 10302 (2000)]Comment: 27 pages, 7 figures, revised version for publication, Physical Review
A (August 2000); major changes, in parts rewritte
Continuous Variable Quantum Cryptography using Two-Way Quantum Communication
Quantum cryptography has been recently extended to continuous variable
systems, e.g., the bosonic modes of the electromagnetic field. In particular,
several cryptographic protocols have been proposed and experimentally
implemented using bosonic modes with Gaussian statistics. Such protocols have
shown the possibility of reaching very high secret-key rates, even in the
presence of strong losses in the quantum communication channel. Despite this
robustness to loss, their security can be affected by more general attacks
where extra Gaussian noise is introduced by the eavesdropper. In this general
scenario we show a "hardware solution" for enhancing the security thresholds of
these protocols. This is possible by extending them to a two-way quantum
communication where subsequent uses of the quantum channel are suitably
combined. In the resulting two-way schemes, one of the honest parties assists
the secret encoding of the other with the chance of a non-trivial superadditive
enhancement of the security thresholds. Such results enable the extension of
quantum cryptography to more complex quantum communications.Comment: 12 pages, 7 figures, REVTe
Bose-Einstein condensates in a double well: mean-field chaos and multi-particle entanglement
A recent publication [Phys. Rev. Lett. 100, 140408 (2008)] shows that there
is a relation between mean-field chaos and multi-particle entanglement for BECs
in a periodically shaken double well. 'Schrodinger-cat' like mesoscopic
superpositions in phase-space occur for conditions for which the system
displays mean-field chaos. In the present manuscript, more general
highly-entangled states are investigated. Mean-field chaos accelerates the
emergence of multi-particle entanglement; the boundaries of stable regions are
particularly suited for entanglement generation.Comment: 5 Pages, 5 jpg-figures, to be published in the proceedings of the
LPHYS0
Slow epidemic extinction in populations with heterogeneous infection rates
We explore how heterogeneity in the intensity of interactions between people
affects epidemic spreading. For that, we study the
susceptible-infected-susceptible model on a complex network, where a link
connecting individuals and is endowed with an infection rate
proportional to the intensity of their contact
, with a distribution taken from face-to-face experiments
analyzed in Cattuto (PLoS ONE 5, e11596, 2010). We find an extremely
slow decay of the fraction of infected individuals, for a wide range of the
control parameter . Using a distribution of width we identify two
large regions in the space with anomalous behaviors, which are
reminiscent of rare region effects (Griffiths phases) found in models with
quenched disorder. We show that the slow approach to extinction is caused by
isolated small groups of highly interacting individuals, which keep epidemic
alive for very long times. A mean-field approximation and a percolation
approach capture with very good accuracy the absorbing-active transition line
for weak (small ) and strong (large ) disorder, respectively
Optical implementation and entanglement distribution in Gaussian valence bond states
We study Gaussian valence bond states of continuous variable systems,
obtained as the outputs of projection operations from an ancillary space of M
infinitely entangled bonds connecting neighboring sites, applied at each of
sites of an harmonic chain. The entanglement distribution in Gaussian valence
bond states can be controlled by varying the input amount of entanglement
engineered in a (2M+1)-mode Gaussian state known as the building block, which
is isomorphic to the projector applied at a given site. We show how this
mechanism can be interpreted in terms of multiple entanglement swapping from
the chain of ancillary bonds, through the building blocks. We provide optical
schemes to produce bisymmetric three-mode Gaussian building blocks (which
correspond to a single bond, M=1), and study the entanglement structure in the
output Gaussian valence bond states. The usefulness of such states for quantum
communication protocols with continuous variables, like telecloning and
teleportation networks, is finally discussed.Comment: 15 pages, 6 figures. To appear in Optics and Spectroscopy, special
issue for ICQO'2006 (Minsk). This preprint contains extra material with
respect to the journal versio
Constraint optimization and landscapes
We describe an effective landscape introduced in [1] for the analysis of
Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph
Coloring. This geometric construction reexpresses these problems in the more
familiar terms of optimization in rugged energy landscapes. In particular, it
allows one to understand the puzzling fact that unsophisticated programs are
successful well beyond what was considered to be the `hard' transition, and
suggests an algorithm defining a new, higher, easy-hard frontier.Comment: Contribution to STATPHYS2
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