821 research outputs found
An H-theorem for the Brownian motion on the hyperbolic plane
We prove an 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 -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 -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
- …