Distinguishability notion based on Wootters statistical distance : Application to discrete maps

We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d for an arbitrary discrete map. Moreover, from d, we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the metric d, which allows us to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and analytically, and we obtain d and the wandering set for some characteristic values of their parameters. Finally, an extension of the metric space associated for arbitrary probability distributions (not necessarily invariant densities) is given along with some consequences. The statistical properties of distributions given by histograms are characterized in terms of the cardinal of the associated metric space. For two conjugate variables, the uncertainty principle is expressed in terms of the diameters of the associated metric space with those variables.Instituto de Física La Plat

Aspectos epistemológicos e históricos de la precisión en las mediciones en física

Fil: Rodríguez, Víctor. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Escuela de Filosofía; Argentina.Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación (FAMAF); Argentina.Fil: Lamberti, Pedro Walter. Ministerio de Ciencia, Tecnología e Innovación de la Nación. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET); Argentina.Este trabajo pretende focalizarse en la dinámica de las mediciones de alta precisión en el ámbito de la metrología contemporánea y de la física experimental. El enfoque se realiza bajo la hipótesis de que la evolución de las mismas conlleva un conjunto de cuestiones conceptuales y de prácticas experimentales que ofrecen un amplio abanico de temas de interés para la consideración epistemológica. Como ha sido dicho con frecuencia, con mejores instrumentos para medir, uno puede ver donde nadie ha visto, es decir, esta acción lleva el germen de nuevos conocimientos. Lo interesante, desde nuestro punto de vista, es que las prácticas de medir enriquecen la epistemología de la experimentación con matices propios de la vida de los laboratorios. En particular, entendemos que actualmente se asiste a un despliegue artesanal extraordinario en el ámbito de los laboratorios especializados alrededor del mundo. Ello constituye un arma de doble filo. Por un lado, refuerza claramente la presencia de la tecnología en las investigaciones y aplicaciones, pero por otra parte, contribuye a ocultar el alcance filosófico de las nuevas maneras de caracterizar algunos fenómenos físicos y químicos a la luz de estas prácticas y de estos nuevos instrumentos. En ellos, la creatividad al servicio de la artesanía y la invención en el campo de la medición eclipsan un modo tradicional de interpretar los procedimientos de medir.Fil: Rodríguez, Víctor. Universidad Nacional de Córdoba. Facultad de Filosofía y Humanidades. Escuela de Filosofía; Argentina.Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación (FAMAF); Argentina.Fil: Lamberti, Pedro Walter. Ministerio de Ciencia, Tecnología e Innovación de la Nación. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET); Argentina.Filosofía, Historia y Filosofía de la Ciencia y la Tecnologí

Relatividad General: de la abstracción a la tecnología

La teoría de la relatividad general de Einstein, de 1916, es una de las grandes producciones científicas del siglo XX y probablemente uno de los símbolos más representativos del nivel de abstracción y profundidad del conocimiento científico. Esta influencia simbólica ha trascendido las fronteras de la física y ha impregnado varios sectores de la cultura general. En este sentido, se ha asociado su estructura y alcance a niveles de, sofisticación sólo alcanzados por pocas obras producidas por el intelecto humano

Hermann Weyl and the gauge

Se hace en este trabajo una aproximación conceptual a la noción de gauge introducida por Hermann Weyl, contextualizada en su origen clásico en la segunda década del siglo XX, con un breve comentario sobre su posterior inserción en la mecánica cuántica de la década siguiente, cuando el área estaba consolidándose. Considerando que es conveniente dar para ello un ámbito adecuado en el que es importante atender al estilo de pensamiento de su autor, se presenta un breve perfil del mismo. Se atiende a sus intereses físicos y filosóficos sin dejar de lado su principal tarea profesional como matemático. El punto de vista adoptado sugiere que no es posible comprender en su integridad el pensamiento de este autor si no se contemplan sus facetas relacionadas con estos tres grandes campos disciplinares. Aunque este objetivo en su plenitud escapa por su extensión y sutilezas a este trabajo, se supone que una aproximación introductoria al caso histórico puede contribuir a una mejor comprensión de su alcance posterior, tal como aparece en las numerosas aplicaciones de este concepto en investigaciones contemporáneas vinculadas con la física de partículas elementales.A conceptual approach to the notion of gauge, mainly due to Hermann Weyl, is developed in this work. Its classical origin in the second decade of the XX century is particularly emphasized, with a brief omment on its posterior insertion in quantum mechanics during the following decade, when this area was emerging. Considering that it is convenient for this purpose to give an adequate framework in which the style of thought of the author is taken into account, a brief profile of it is presented. His physical and philosophical motivations are expounded, but attending to the fact that his main work has been as a professional mathematician. The adopted point of view suggests that it is not possible to comprehend the integrity of his thought without analyzing the aspects related to these three big disciplinary fields. Even though this integral goal is out of the scope of this work, it is assumed that an introduction to the historical case may contribute to a better understanding of its later use, such as it figures in numerous applications of this concept in contemporary researches related to elementary particle physics.Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Rodriguez, Victor Ruben. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin

Correlations in Two-Qubit Systems under non-dissipative decoherence

We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D. As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.Fil: Bussandri, Diego. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Osán, Tristán Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Majtey, Ana Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Comment on "Quantum Kaniadakis entropy under projective measurement"

We comment on the main result given by Ourabah et al. [Phys. Rev. E 92, 032114 (2015)PLEEE81539-375510.1103/PhysRevE.92.032114], noting that it can be derived as a special case of the more general study that we have provided in [Quantum Inf Process 15, 3393 (2016)10.1007/s11128-016-1329-5]. Our proof of the nondecreasing character under projective measurements of so-called generalized (h,φ) entropies (that comprise the Kaniadakis family as a particular case) has been based on majorization and Schur-concavity arguments. As a consequence, we have obtained that this property is obviously satisfied by Kaniadakis entropy but at the same time is fulfilled by all entropies preserving majorization. In addition, we have seen that our result holds for any bistochastic map, being a projective measurement a particular case. We argue here that looking at these facts from the point of view given in [Quantum Inf Process 15, 3393 (2016)10.1007/s11128-016-1329-5] not only simplifies the demonstrations but allows for a deeper understanding of the entropic properties involved.Instituto de Física La Plat

A family of generalized quantum entropies: definition and properties

We present a quantum version of the generalized (h, φ)-entropies, introduced by Salicrú et al. for the study of classical probability distributions.We establish their basic properties and show that already known quantum entropies such as von Neumann, and quantum versions of Rényi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicrú form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum (h, φ)-entropies under the action of quantum operations and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement and introduce a discussion on possible generalized conditional entropies as well.Facultad de Ciencias ExactasInstituto de Física La Plat

Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures

We provide a twofold extension of Landau-Pollak uncertainty relations for mixed quantum states and for positive operator-valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner product between the states. The triangle inequality satisfied by such metrics plays a crucial role in our derivation. The usual Landau-Pollak inequality is thus a particular case (derived from Wootters metric) of the family of inequalities obtained, and, moreover, we show that it is the most restrictive relation within the family.Instituto de Física La Plat

Detecting dynamical changes in time series by using the Jensen Shannon divergence

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult because they have a common wide band power spectrum, a delta like autocorrelation function, and share other features as well. In general, signals are presented as continuous records and require to be discretized for being analyzed. In this work, we introduce different schemes for discretizing and for detecting dynamical changes in time series. One of the main motivations is to detect transitions between the chaotic and random regime. The tools here used here originate from the Information Theory. The schemes proposed are applied to simulated and real life signals, showing in all cases a high proficiency for detecting changes in the dynamics of the associated time series.Fil: Mateos, Diego Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. University Of Toronto. Hospital For Sick Children; CanadáFil: Riveaud, Leonardo Esteban. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin

H-theorems for the Brownian motion on the hyperbolic plane

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