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A. Plastino

Publications and source records attributed to A. Plastino.

At least 109 records · Page 6Linked to original sources
arXiv2011

Properties of a geometric measure for quantum discord

We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {\bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in representing quantum discord. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario.

quant-ph↗
arXiv2011

Scaled Bregman divergences in a Tsallis scenario

There exist two different versions of the Kullback-Leibler divergence (K-Ld) in Tsallis statistics, namely the usual generalized K-Ld and the generalized Bregman K-Ld. Problems have been encountered in trying to reconcile them. A condition for consistency between these two generalized K-Ld-forms by recourse to the additive duality of Tsallis statistics is derived. It is also shown that the usual generalized K-Ld subjected to this additive duality, known as the dual generalized K-Ld, is a scaled Bregman divergence. This leads to an interesting conclusion: the dual generalized mutual information is a scaled Bregman information. The utility and implications of these results are discussed.

cond-mat.stat-mech↗
arXiv2011

Entropic Entanglement Criteria for Fermion Systems

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one particle reduced density matrix, on the other one. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi's entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi's entropic parameter is investigated. The extension of these criteria to systems of $N$ identical fermions is also considered.

quant-ph↗
arXiv2011

Deformed Statistics Free Energy Model for Source Separation using Unsupervised Learning

A generalized-statistics variational principle for source separation is formulated by recourse to Tsallis' entropy subjected to the additive duality and employing constraints described by normal averages. The variational principle is amalgamated with Hopfield-like learning rules resulting in an unsupervised learning model. The update rules are formulated with the aid of q-deformed calculus. Numerical examples exemplify the efficacy of this model.

cond-mat.stat-mech↗
arXiv2011

Dynamics of the intensity-dependent Jaynes-Cummings model analyzed via Fisher information

The dynamics of the Buck and Sukumar model [B. Buck and C.V. Sukumar, Phys. Lett. A 81 (1981) 132] are investigated using different semi-classical information-theory tools. Interesting aspects of the periodicity inherent to the model are revealed and somewhat unexpected features are revealed that seem to be related to the classical-quantum transition.

quant-ph↗
arXiv2011

Legendre-transform structure derived from quantum theorems

By recourse to i) the Hellmann-Feynman theorem and ii) the Virial one, the information-optimizing principle based on Fisher's information measure uncovers a Legendre-transform structure associated with Schrödinger's equation, in close analogy with the structure that lies behind the standard thermodynamical formalism. The present developments provide new evidence for the information theoretical links based on Fisher's measure that exist between Schrödinger's equation, on the one hand, and thermodynamics/thermostatistics on the other one.

cond-mat.stat-mech↗
arXiv2010

A direct proof of Jauregui-Tsallis' conjecture

We give here direct proof of a recent conjecture of Jauregui and Tsallis about a new representation of Dirac's delta distribution by means of q-exponentials. The proof is based in the use of tempered ultradistributions' theory.

math-ph↗
arXiv2010

Entropic Upper Bound on Gravitational Binding Energy

We prove that the gravitational binding energy Ω of a self gravitating system described by a mass density distribution ρ(x) admits an upper bound B[ρ(x)] given by a simple function of an appropriate, non-additive Tsallis' power-law entropic functional Sq evaluated on the density ρ. The density distributions that saturate the entropic bound have the form of isotropic q-Gaussian distributions. These maximizer distributions correspond to the Plummer density profile, well known in astrophysics. A heuristic scaling argument is advanced suggesting that the entropic bound B[ρ(x)] is unique, in the sense that it is unlikely that exhaustive entropic upper bounds not based on the alluded Sq entropic measure exit. The present findings provide a new link between the physics of self gravitating systems, on the one hand, and the statistical formalism associated with non-additive, power-law entropic measures, on the other hand.

cond-mat.stat-mech↗
arXiv2010

Quantum Potentials with q-Gaussian Ground States

We determine families of spherically symmetrical $D$-dimensional quantum potential functions $V(r)$ having ground state wavefunctions that exhibit, either in configuration or in momentum space, the form of an isotropic $q$-Gaussian. These wavefunctions admit a maximum entropy description in terms of $S_q$ power-law entropies. We show that the potentials with a ground state of the $q$-Gaussian form in momentum space admit the Coulomb potential $-1/r$ as a particular instance. Furthermore, all these potentials behave asymptotically as the Coulomb potential for large $r$for all values of the parameter $q$ such that $0<q<1.$

cond-mat.stat-mech↗
arXiv2010

Some features of the state-space trajectories followed by robust entangled four-qubit states during decoherence

In a recent work (Borras et al., Phys. Rev. A {\bf 79}, 022108 (2009)), we have determined, for various decoherence channels, four-qubit initial states exhibiting the most robust possible entanglement. Here we explore some geometrical features of the trajectories in state space generated by the decoherence process, connecting the initially robust pure state with the completely decohered mixed state obtained at the end of the evolution. We characterize these trajectories by recourse to the distance between the concomitant time dependent mixed state and different reference states.

quant-ph↗
arXiv2010

Generalized Statistics Variational Perturbation Approximation using q-Deformed Calculus

A principled framework to generalize variational perturbation approximations (VPA's) formulated within the ambit of the nonadditive statistics of Tsallis statistics, is introduced. This is accomplished by operating on the terms constituting the perturbation expansion of the generalized free energy (GFE) with a variational procedure formulated using \emph{q-deformed calculus}. A candidate \textit{q-deformed} generalized VPA (GVPA) is derived with the aid of the Hellmann-Feynman theorem. The generalized Bogoliubov inequality for the approximate GFE are derived for the case of canonical probability densities that maximize the Tsallis entropy. Numerical examples demonstrating the application of the \textit{q-deformed} GVPA are presented. The qualitative distinctions between the \textit{q-deformed} GVPA model \textit{vis-á-vis} prior GVPA models are highlighted.

cond-mat.stat-mech↗
arXiv2009

Unravelling the size distribution of social groups with information theory on complex networks

The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E {\bf 60} 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale invariant systems and classical gases [arXiv:0908.0504]. Going beyond the ideal gas scenario is seen to be tantamount to simulating the interactions taking place in a network's competitive cluster growth process. We find a scaling rule that allows to classify the final cluster-size distributions using only one parameter that we call the competitiveness. Empirical city-size distributions and electoral results can be thus reproduced and classified according to this competitiveness, which also allows to correctly predict well-established assessments such as the "six-degrees of separation", which is shown here to be a direct consequence of the maximum number of stable social relationships that one person can maintain, known as Dunbar's number. Finally, we show that scaled city-size distributions of large countries follow the same universal distribution.

physics.soc-ph↗
arXiv2009

Subspace modelling for structured noise suppression

The problem of structured noise suppression is addressed by i)modelling the subspaces hosting the components of the signal conveying the information and ii)applying a non-extensive nonlinear technique for effecting the right separation. Although the approach is applicable to all situations satisfying the hypothesis of the proposed framework, this work is motivated by a particular scenario, namely, the cancellation of low frequency noise in broadband seismic signals.

math-ph↗
arXiv2009

Fisher-information and the thermodynamics of scale-invariant systems

We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of Fisher's information measure. In such a way a clear analogy between these systems's thermal properties and those of gases and fluids is seen to emerge in natural fashion. We focus attention on the non-interacting scenario, speaking thus of scale-free ideal gases (SFIGs) and present some empirical evidences regarding such disparate systems as electoral results, city populations and total citations in Physics journals, that seem to indicate that SFIGs do exist. We also illustrate the way in which Zipf's law can be understood in a thermodynamical context as the surface of a finite system. Finally, we derive an equivalent microscopic description of our systems which totally agrees with previous numerical simulations found in the literature.

physics.soc-ph↗
arXiv2009

Zipf's law from a Fisher variational-principle

Zipf's law is shown to arise as the variational solution of a problem formulated in Fisher's terms. An appropriate minimization process involving Fisher information and scale-invariance yields this universal rank distribution. As an example we show that the number of citations found in the most referenced physics journals follows this law.

physics.soc-ph↗
arXiv2009

Entropic descriptor of a complex behaviour

We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum possible value Smax and its minimum possible value Smin. When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly non-trivial, length-scale dependence of the entropic descriptor makes it an adequate complexity-measure, able to distinguish between structurally distinct configurational macrostates with the same degree of disorder.

cond-mat.stat-mech↗
arXiv2009

Deformed Statistics Formulation of the Information Bottleneck Method

The theoretical basis for a candidate variational principle for the information bottleneck (IB) method is formulated within the ambit of the generalized nonadditive statistics of Tsallis. Given a nonadditivity parameter $ q $, the role of the \textit{additive duality} of nonadditive statistics ($ q^*=2-q $) in relating Tsallis entropies for ranges of the nonadditivity parameter $ q < 1 $ and $ q > 1 $ is described. Defining $ X $, $ \tilde X $, and $ Y $ to be the source alphabet, the compressed reproduction alphabet, and, the \textit{relevance variable} respectively, it is demonstrated that minimization of a generalized IB (gIB) Lagrangian defined in terms of the nonadditivity parameter $ q^* $ self-consistently yields the \textit{nonadditive effective distortion measure} to be the \textit{$ q $-deformed} generalized Kullback-Leibler divergence: $ D_{K-L}^{q}[p(Y|X)||p(Y|\tilde X)] $. This result is achieved without enforcing any \textit{a-priori} assumptions. Next, it is proven that the $q^*-deformed $ nonadditive free energy of the system is non-negative and convex. Finally, the update equations for the gIB method are derived. These results generalize critical features of the IB method to the case of Tsallis statistics.

cond-mat.stat-mech↗