452 research outputs found
Simplifying Random Satisfiability Problem by Removing Frustrating Interactions
How can we remove some interactions in a constraint satisfaction problem
(CSP) such that it still remains satisfiable? In this paper we study a modified
survey propagation algorithm that enables us to address this question for a
prototypical CSP, i.e. random K-satisfiability problem. The average number of
removed interactions is controlled by a tuning parameter in the algorithm. If
the original problem is satisfiable then we are able to construct satisfiable
subproblems ranging from the original one to a minimal one with minimum
possible number of interactions. The minimal satisfiable subproblems will
provide directly the solutions of the original problem.Comment: 21 pages, 16 figure
Memory effects in attenuation and amplification quantum processes
With increasing communication rates via quantum channels, memory effects
become unavoidable whenever the use rate of the channel is comparable to the
typical relaxation time of the channel environment. We introduce a model of a
bosonic memory channel, describing correlated noise effects in quantum-optical
processes via attenuating or amplifying media. To study such a channel model,
we make use of a proper set of collective field variables, which allows us to
unravel the memory effects, mapping the n-fold concatenation of the memory
channel to a unitarily equivalent, direct product of n single-mode bosonic
channels. We hence estimate the channel capacities by relying on known results
for the memoryless setting. Our findings show that the model is characterized
by two different regimes, in which the cross correlations induced by the noise
among different channel uses are either exponentially enhanced or exponentially
reduced.Comment: 10 pages, 7 figures, close to the published versio
Asymmetric quantum error correcting codes
The noise in physical qubits is fundamentally asymmetric: in most devices,
phase errors are much more probable than bit flips. We propose a quantum error
correcting code which takes advantage of this asymmetry and shows good
performance at a relatively small cost in redundancy, requiring less than a
doubling of the number of physical qubits for error correction
Information transmission through lossy bosonic memory channels
We study the information transmission through a quantum channel, defined over
a continuous alphabet and losing its energy en route, in presence of correlated
noise among different channel uses. We then show that entangled inputs improve
the rate of transmission of such a channel.Comment: 6 pages revtex, 2 eps figure
Effective Capacity in Broadcast Channels with Arbitrary Inputs
We consider a broadcast scenario where one transmitter communicates with two
receivers under quality-of-service constraints. The transmitter initially
employs superposition coding strategies with arbitrarily distributed signals
and sends data to both receivers. Regarding the channel state conditions, the
receivers perform successive interference cancellation to decode their own
data. We express the effective capacity region that provides the maximum
allowable sustainable data arrival rate region at the transmitter buffer or
buffers. Given an average transmission power limit, we provide a two-step
approach to obtain the optimal power allocation policies that maximize the
effective capacity region. Then, we characterize the optimal decoding regions
at the receivers in the space spanned by the channel fading power values. We
finally substantiate our results with numerical presentations.Comment: This paper will appear in 14th International Conference on
Wired&Wireless Internet Communications (WWIC
Entropy landscape and non-Gibbs solutions in constraint satisfaction problems
We study the entropy landscape of solutions for the bicoloring problem in
random graphs, a representative difficult constraint satisfaction problem. Our
goal is to classify which type of clusters of solutions are addressed by
different algorithms. In the first part of the study we use the cavity method
to obtain the number of clusters with a given internal entropy and determine
the phase diagram of the problem, e.g. dynamical, rigidity and SAT-UNSAT
transitions. In the second part of the paper we analyze different algorithms
and locate their behavior in the entropy landscape of the problem. For instance
we show that a smoothed version of a decimation strategy based on Belief
Propagation is able to find solutions belonging to sub-dominant clusters even
beyond the so called rigidity transition where the thermodynamically relevant
clusters become frozen. These non-equilibrium solutions belong to the most
probable unfrozen clusters.Comment: 38 pages, 10 figure
Exceeding classical capacity limit in quantum optical channel
The amount of information transmissible through a communications channel is
determined by the noise characteristics of the channel and by the quantities of
available transmission resources. In classical information theory, the amount
of transmissible information can be increased twice at most when the
transmission resource (e.g. the code length, the bandwidth, the signal power)
is doubled for fixed noise characteristics. In quantum information theory,
however, the amount of information transmitted can increase even more than
twice. We present a proof-of-principle demonstration of this super-additivity
of classical capacity of a quantum channel by using the ternary symmetric
states of a single photon, and by event selection from a weak coherent light
source. We also show how the super-additive coding gain, even in a small code
length, can boost the communication performance of conventional coding
technique.Comment: 4 pages, 3 figure
Implementation of generalized quantum measurements: superadditive quantum coding, accessible information extraction, and classical capacity limit
Quantum information theory predicts that when the transmission resource is
doubled in quantum channels, the amount of information transmitted can be
increased more than twice by quantum channel coding technique, whereas the
increase is at most twice in classical information theory. This remarkable
feature, the superadditive quantum coding gain, can be implemented by
appropriate choices of code words and corresponding quantum decoding which
requires a collective quantum measurement. Recently, the first experimental
demonstration was reported [Phys. Rev. Lett. 90, 167906 (2003)]. The purpose of
this paper is to describe our experiment in detail. Particularly, a design
strategy of quantum collective decoding in physical quantum circuits is
emphasized. We also address the practical implication of the gain on
communication performance by introducing the quantum-classical hybrid coding
scheme. We show how the superadditive quantum coding gain, even in a small code
length, can boost the communication performance of conventional coding
technique.Comment: 15 pages, 14 figure
One-mode Bosonic Gaussian channels: a full weak-degradability classification
A complete degradability analysis of one-mode Gaussian Bosonic channels is
presented. We show that apart from the class of channels which are unitarily
equivalent to the channels with additive classical noise, these maps can be
characterized in terms of weak- and/or anti-degradability. Furthermore a new
set of channels which have null quantum capacity is identified. This is done by
exploiting the composition rules of one-mode Gaussian maps and the fact that
anti-degradable channels can not be used to transfer quantum information.Comment: 23 pages, 3 figure
Information capacity in the weak-signal approximation
We derive an approximate expression for mutual information in a broad class
of discrete-time stationary channels with continuous input, under the
constraint of vanishing input amplitude or power. The approximation describes
the input by its covariance matrix, while the channel properties are described
by the Fisher information matrix. This separation of input and channel
properties allows us to analyze the optimality conditions in a convenient way.
We show that input correlations in memoryless channels do not affect channel
capacity since their effect decreases fast with vanishing input amplitude or
power. On the other hand, for channels with memory, properly matching the input
covariances to the dependence structure of the noise may lead to almost
noiseless information transfer, even for intermediate values of the noise
correlations. Since many model systems described in mathematical neuroscience
and biophysics operate in the high noise regime and weak-signal conditions, we
believe, that the described results are of potential interest also to
researchers in these areas.Comment: 11 pages, 4 figures; accepted for publication in Physical Review
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