3,358 research outputs found
A rigorous analysis of the cavity equations for the minimum spanning tree
We analyze a new general representation for the Minimum Weight Steiner Tree
(MST) problem which translates the topological connectivity constraint into a
set of local conditions which can be analyzed by the so called cavity equations
techniques. For the limit case of the Spanning tree we prove that the fixed
point of the algorithm arising from the cavity equations leads to the global
optimum.Comment: 5 pages, 1 figur
On Strong Superadditivity of the Entanglement of Formation
We employ a basic formalism from convex analysis to show a simple relation
between the entanglement of formation and the conjugate function of
the entanglement function E(\rho)=S(\trace_A\rho). We then consider the
conjectured strong superadditivity of the entanglement of formation , where and are the
reductions of to the different Hilbert space copies, and prove that it
is equivalent with subadditivity of . As an application, we show that
strong superadditivity would follow from multiplicativity of the maximal
channel output purity for all non-trace-preserving quantum channels, when
purity is measured by Schatten -norms for tending to 1.Comment: 11 pages; refs added, explanatory improvement
Inference and learning in sparse systems with multiple states
We discuss how inference can be performed when data are sampled from the
non-ergodic phase of systems with multiple attractors. We take as model system
the finite connectivity Hopfield model in the memory phase and suggest a cavity
method approach to reconstruct the couplings when the data are separately
sampled from few attractor states. We also show how the inference results can
be converted into a learning protocol for neural networks in which patterns are
presented through weak external fields. The protocol is simple and fully local,
and is able to store patterns with a finite overlap with the input patterns
without ever reaching a spin glass phase where all memories are lost.Comment: 15 pages, 10 figures, to be published in Phys. Rev.
Squeezing as an irreducible resource
We show that squeezing is an irreducible resource which remains invariant
under transformations by linear optical elements. In particular, we give a
decomposition of any optical circuit with linear input-output relations into a
linear multiport interferometer followed by a unique set of single mode
squeezers and then another multiport interferometer. Using this decomposition
we derive a no-go theorem for superpositions of macroscopically distinct states
from single-photon detection. Further, we demonstrate the equivalence between
several schemes for randomly creating polarization-entangled states. Finally,
we derive minimal quantum optical circuits for ideal quantum non-demolition
coupling of quadrature-phase amplitudes.Comment: 4 pages, 3 figures, new title, removed the fat
Encoding for the Blackwell Channel with Reinforced Belief Propagation
A key idea in coding for the broadcast channel (BC) is binning, in which the
transmitter encode information by selecting a codeword from an appropriate bin
(the messages are thus the bin indexes). This selection is normally done by
solving an appropriate (possibly difficult) combinatorial problem. Recently it
has been shown that binning for the Blackwell channel --a particular BC-- can
be done by iterative schemes based on Survey Propagation (SP). This method uses
decimation for SP and suffers a complexity of O(n^2). In this paper we propose
a new variation of the Belief Propagation (BP) algorithm, named Reinforced BP
algorithm, that turns BP into a solver. Our simulations show that this new
algorithm has complexity O(n log n). Using this new algorithm together with a
non-linear coding scheme, we can efficiently achieve rates close to the border
of the capacity region of the Blackwell channel.Comment: 5 pages, 8 figures, submitted to ISIT 200
Large deviations of cascade processes on graphs
Simple models of irreversible dynamical processes such as Bootstrap
Percolation have been successfully applied to describe cascade processes in a
large variety of different contexts. However, the problem of analyzing
non-typical trajectories, which can be crucial for the understanding of the
out-of-equilibrium phenomena, is still considered to be intractable in most
cases. Here we introduce an efficient method to find and analyze optimized
trajectories of cascade processes. We show that for a wide class of
irreversible dynamical rules, this problem can be solved efficiently on
large-scale systems
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
Optimal Control Theory for Continuous Variable Quantum Gates
We apply the methodology of optimal control theory to the problem of
implementing quantum gates in continuous variable systems with quadratic
Hamiltonians. We demonstrate that it is possible to define a fidelity measure
for continuous variable (CV) gate optimization that is devoid of traps, such
that the search for optimal control fields using local algorithms will not be
hindered. The optimal control of several quantum computing gates, as well as
that of algorithms composed of these primitives, is investigated using several
typical physical models and compared for discrete and continuous quantum
systems. Numerical simulations indicate that the optimization of generic CV
quantum gates is inherently more expensive than that of generic discrete
variable quantum gates, and that the exact-time controllability of CV systems
plays an important role in determining the maximum achievable gate fidelity.
The resulting optimal control fields typically display more complicated Fourier
spectra that suggest a richer variety of possible control mechanisms. Moreover,
the ability to control interactions between qunits is important for delimiting
the total control fluence. The comparative ability of current experimental
protocols to implement such time-dependent controls may help determine which
physical incarnations of CV quantum information processing will be the easiest
to implement with optimal fidelity.Comment: 39 pages, 11 figure
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