arXiv subjects

A. Plastino

Publications and source records attributed to A. Plastino.

At least 127 records · Page 7Linked to original sources

arXiv2009

Generalized Statistics Framework for Rate Distortion Theory

Variational principles for the rate distortion (RD) theory in lossy compression are formulated within the ambit of the generalized nonextensive statistics of Tsallis, for values of the nonextensivity parameter satisfying $ 0 < q < 1 $ and $ q > 1 $. Alternating minimization numerical schemes to evaluate the nonextensive RD function, are derived. Numerical simulations demonstrate the efficacy of generalized statistics RD models.

cond-mat.stat-mech↗

arXiv2009

Geometry of the Central Limit Theorem in the Nonextensive Case

We uncover geometric aspects that underlie the sum of two independent stochastic variables when both are governed by q-Gaussian probability distributions. The pertinent discussion is given in terms of random vectors uniformly distributed on a p-sphere.

cond-mat.stat-mech↗

arXiv2008

Tsallis' deformation parameter q quantifies the classical-quantum transition

We investigate the classical limit of a type of semiclassical evolution, the pertinent system representing the interaction between matter and a given field. On using as a quantifier of the ensuing dynamics Tsallis q-entropy, we encounter that it not only appropriately describes the quantum-classical transition, but that the associated deformation-parameter q itself characterizes the different regimes involved in the process, detecting the most salient fine details of the changeover.

cond-mat.stat-mech↗

arXiv2008

Robustness of Highly Entangled Multi-Qubit States Under Decoherence

We investigate the decay of entanglement, due to decoherence, of multi-qubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own, independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness optimization problem, only involving states equivalent under local unitary transformations to the |GHZ> state.

quant-ph↗

arXiv2008

Quantifiers for randomness of chaotic pseudo random number generators

We deal with randomness-quantifiers and concentrate on their ability do discern the hallmark of chaos in time-series used in connection with pseudo random number generators (PRNG). Workers in the field are motivated to use chaotic maps for generating PRNGs because of the simplicity of their implementation. Although there exist very efficient general-purpose benchmarks for testing PRNGs, we feel that the analysis provided here sheds additional didactic light on the importance of the main statistical characteristics of a chaotic map, namely, i) its invariant measure and ii) the mixing constant. This is of help in answering two questions that arise in applications, that is, (1) which is the best PRNG among the available ones? and (2) If a given PRNG turns out not to be good enough and a randomization procedure must still be applied to it, which is the best applicable randomization procedure?. Our answer provides a comparative analysis of several quantifiers advanced in the extant literature.

nlin.CD↗

arXiv2008

Aspects of quantum phase transitions

A unified description of i) classical phase transitions and their remnants in finite systems and ii) quantum phase transitions is presented. The ensuing discussion relies on the interplay between, on the one hand, the thermodynamic concepts of temperature and specific heat and on the other, the quantal ones of coupling strengths in the Hamiltonian. Our considerations are illustrated in an exactly solvable model of Plastino and Moszkowski [Il Nuovo Cimento {\bf 47}, 470 (1978)].

quant-ph↗

arXiv2008

On the metric character of the quantum Jensen-Shannon divergence

In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (Phys. Rev. A 72, 052310 (2005)). This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of simulations for mixed states, that its square root verifies the triangle inequality.

quant-ph↗

arXiv2008

Jensen Shannon divergence as a measure of the degree of entanglement

The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJSD) between quantum states. Here we study this distance as a geometrical measure of entanglement and apply it to different families of states.

quant-ph↗

arXiv2008

Some Entanglement Features of Highly Entangled Multiqubit States

We explore some basic entanglement features of multiqubit systems that are relevant for the development of algorithms for searching highly entangled states. In particular, we compare the behaviours of multiqubit entanglement measures based (i) on the von Neumann entropy of marginal density matrices and (ii) on the linear entropy of those matrices.

quant-ph↗

arXiv2008

Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution

A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multi-qubits states. In particular, our present results are compared with those recently reported by Brown et al. [J. Phys. A: Math. Gen. 38 (2005) 1119]. The statistical distribution of entanglement values for the aforementioned multi-qubit systems is also explored.

quant-ph↗

arXiv2008

Entanglement and the Quantum Brachistochrone Problem

Entanglement is closely related to some fundamental features of the dynamics of composite quantum systems: quantum entanglement enhances the "speed" of evolution of certain quantum states, as measured by the time required to reach an orthogonal state. The concept of "speed" of quantum evolution constitutes an important ingredient in any attempt to determine the fundamental limits that basic physical laws impose on how fast a physical system can process or transmit information. Here we explore the relationship between entanglement and the speed of quantum evolution in the context of the quantum brachistochrone problem. Given an initial and a final state of a composite system we consider the amount of entanglement associated with the brachistochrone evolution between those states, showing that entanglement is an essential resource to achieve the alluded time-optimal quantum evolution.

quant-ph↗

arXiv2007

Semiclassical statistical mechanics' tools for deformed algebras

In order to enlarge the present arsenal of semiclassical toools we explicitly obtain here the Husimi distributions and Wehrl entropy within the context of deformed algebras built up on the basis of a new family of q-deformed coherent states, those of Quesne [J. Phys. A 35, 9213 (2002)]. We introduce also a generalization of the Wehrl entropy constructed with escort distributions. The two generalizations are investigated with emphasis on i) their behavior as a function of temperature and ii) the results obtained when the deformation-parameter tends to unity.

cond-mat.stat-mech↗

arXiv2007

Detecting q-Gaussian distributions and the normalization effect

We show that whenever data are gathered using a device that performs a normalization-preprocessing, the ensuing normalized input, as recorded by the measurement device, will always be q-Gaussian distributed if the incoming data exhibit elliptical symmetry. As a consequence, great care should be exercised when detecting q-Gaussians. As an example, Gaussian data will appear, after normalization, in the guise of q-Gaussian records. Moreover, we show that the value of the resulting parameter q can be deduced from the normalization technique that characterizes the device.

cond-mat.stat-mech↗

arXiv2007

Central limit theorem, deformed exponentials and superstatistics

We show that there exists a very natural, superstatistics-linked extension of the central limit theorem (CLT) to deformed exponentials (also called q-Gaussians): This generalization favorably compares with the one provided by S. Umarov and C. Tsallis [arXiv:cond-mat/0703533], since the latter requires a special "q-independence" condition on the data. On the contrary, our CLT proposal applies exactly in the usual conditions in which the classical CLT is used. Moreover, we show that, asymptotically, the q-independence condition is naturally induced by our version of the CLT.

cond-mat.stat-mech↗

arXiv2006

Scale invariance and related properties of q-Gaussian systems

We advance scale-invariance arguments for systems that are governed (or approximated) by a $q-$Gaussian distribution, i.e., a power law distribution with exponent $Q=1/(1-q); q \in \mathbb{R}$. The ensuing line of reasoning is then compared with that applying for Gaussian distributions, with emphasis on dimensional considerations. In particular, a Gaussian system may be part of a larger system that is not Gaussian, but, if the larger system is spherically invariant, then it is necessarily Gaussian again. We show that this result extends to q-Gaussian systems via elliptic invariance. The problem of estimating the appropriate value for $q$ is revisited. A kinetic application is also provided.

cond-mat.stat-mech↗

arXiv2006

Entanglement and the Lower Bounds on the Speed of Quantum Evolution

The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state $ψ_I$ may need so as to evolve into a state orthogonal to itself. Recently [V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A {\bf 67}, 052109 (2003)] this bound has been generalized to the case where $ψ_I$ does not necessarily evolve into an orthogonal state, but into any other $ψ_F$. It was pointed out that, for certain classes of states, quantum entanglement enhances the evolution "speed" of composite quantum systems. In this work we provide an exhaustive and systematic QSL study for pure and mixed states belonging to the whole 15-dimensional space of two qubits, with $ψ_F$ a not necessarily orthogonal state to $ψ_I$. We display convincing evidence for a clear correlation between concurrence, on the one hand, and the speed of quantum evolution determined by the action of a rather general local Hamiltonian, on the other one.

quant-ph↗

arXiv2006

Delocalization and the semiclassical description of molecular rotation

We discuss phase-space delocalization for the rigid rotator within a semiclassical context by recourse to the Husimi distributions of both the linear and the $3D-$anisotropic instances. Our treatment is based upon the concomitant Fisher information measures. The pertinent Wehrl entropy is also investigated in the linear case.

cond-mat.stat-mech↗

arXiv2006

Power-law random walks

We present some new results about the distribution of a random walk whose independent steps follow a $q-$Gaussian distribution with exponent $\frac{1}{1-q}; q \in \mathbb{R}$. In the case $q>1$ we show that a stochastic representation of the point reached after $n$ steps of the walk can be expressed explicitly for all $n$. In the case $q<1,$ we show that the random walk can be interpreted as a projection of an isotropic random walk, i.e. a random walk with fixed length steps and uniformly distributed directions.

cond-mat.stat-mech↗