INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
congresos y reuniones científicas
Distinguishability notion based on Wootters statistical distance: an application to discrete maps
PEDRO WALTER LAMBERTI; MARIELA PORTESI; IGNACIO S. GOMEZ
Jornada; Jornadas de Fundamentos de Cuántica VI; 2016
CEILAP - CITEDEF, Facultad de Ciencias Exactas (UNLP), Universidad de Buenos Aires (UBA)
Wootters proposed a statistical distance in Hilbert space. Here we study a concept of distinguishability inspired by means of a notion of distance for unidimensional discrete maps and we redefine it as a metric. Moreover, from this metric we associate a metric space to 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.We illustrate in the case of the logistic map and we find the metric numerically for several values of its characteristic parameter. Finally, we propose a generalization to maps of arbitrary dimensions, and illustrate this with a pair of uncoupled logistic maps.