An H-theorem for the Brownian motion on the hyperbolic plane

We prove an $H-$theorem for the Brownian motion on the hyperbolic plane with a drift, as studied by Comtet and Monthus; the entropy used here is not the Boltzmann entropy but the R\'enyi entropy, the parameter of which being related in a simple way to the value of the drift.Comment: Better versio

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.Comment: 5 pages, 2 figures, to appear in the special issue of IJQI "Noise, Information and Complexity at Quantum Scale", eds. S. Mancini and F. Marcheson

A family of generalized quantum entropies: definition and properties

We present a quantum version of the generalized $(h,\phi)$-entropies, introduced by Salicr\'u \textit{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 R\'enyi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicr\'u form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum $(h,\phi)$-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.Comment: 26 pages, 1 figure. Close to published versio

Unified entropic measures of quantum correlations induced by local measurements

We introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of non-additive entropies. In this way, we overcome the issue of the artificial increasing of the value of quantum correlations measures based on non-additive entropies when an uncorrelated ancilla is appended to the system without changing the computability of our entropic correlations measures with respect to the previous ones. Moreover, we recover as limiting cases the quantum correlations measures based on von Neumann and R\'enyi entropies (i.e., additive entropies), for which the adjustment factor becomes trivial. In addition, we distinguish between total and semiquantum correlations and obtain some relations between them. Finally, we obtain analytical expressions of the entropic correlations measures for typical quantum bipartite systems.Comment: 10 pages, 1 figur

Natural Metric for Quantum Information Theory

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.Comment: v2: enlarged; presented at ISIT 2008 (Toronto

Notas sobre la concepción de Maxwell acerca de la fisica experimental

El Laboratorio Cavendish fue inaugurado en 1874 y James Clerk Maxwell fue su primer director. En ese momento Maxwell ocupaba el cargo de Profesor de Física Experimental en la cátedra Cavendish de la Universidad de Cambridge. La creación de este laboratorio tuvo la intención de fortalecer la física experimental en el Reino Unido. Se asocia su creación con la "necesidad de entrenamiento práctico de científicos e ingenieros" tras el éxito de la Gran Exhibición Industrial de 1851, que dejó claramente expuestos los requerimientos de una sociedad industrial. Hasta ese momento, la física en Inglaterra significaba física teórica y se la pensaba en el ámbito de las matemáticas. Hubo mucha especulación sobre la elección del Profesor de Física Experimental. Tanto William Thomson (de Glasgow) como John Rayleigh (de Essex) fueron candidatos con grandes posibilidades, pero ambos rechazaron la oferta Cuando se anunció la designación de Maxwell, hubo cierto asombro (y malestar) en la comunidad científica londinense. El nuevo profesor Maxwell era, por aquel entonces, relativamente desconocido. Su nombramiento como profesor fue anunciado el 8 de marzo de 1871, y más allá de las críticas iniciales, su clase inaugural fue seguida por una gran cantidad de estudiantes e investigadores de Cambridge. Sus libros más influyentes, Teoría Cinética ( 1871) y el Tratado de Electricidad y Magnetismo ( 1873), -no habían sido todavía publicados. En esta clase, Maxwell dejó claramente expuesta la impronta que él darla unos años después al Laboratorio Cavendish, cuando fuera su Director. Una de sus primeras acciones al asumir como Director del laboratorio, fue la construcción de un conjunto de equipos de física experimental, muchos de los cuales eran producto de sus propios desarrollos y concepciones. Entre ellos se destaca un modelo mecánico que tenía por objetivo representar la interacción de dos circuitos eléctricos. El estudio de este modelo es el propósito primordial del presente trabajo. Para una mejor comprensión de los objetivos perseguidos por Maxwell con este tipo de desarrollos, haremos, por un lado una breve descripción de las ideas que Maxwell tenía sobre la física experimental y por el otro, un análisis del modelo desde la concepción mecanicista que él tenía del electromagnetismo

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.Comment: 14 pages, corrected equation 1