Csiszár Quantum Distances

PEDRO W. LAMBERTI; TRISTÁN M. OSÁN; DIEGO G. BUSSANDRI

Capital federal, Buenos Aires

Congreso; Giambiagi Winter School 2016; 2016

Universidad Nacional de Buenos Aires (UBA)

Csiszar´s divergences were introduced as measures of distinguishability between classical probability distributions. The general expression of a Csiszar divergence, for discrete probability distributions p and q is D(p;q) = Sum_i p_i f(qi/pi) with f(x) a convex function such that f(1) = 0. The widely used Kullback-Leibler divergence is an example of them, with f(x) = -log(x). Another examples are the Jensen-Shannon divergence, the Hellinger distance, the triangular discrimination and the variational distance. In this work we proposed a way for extending the Csiszar divergence to the realm of quantum information theory. We studied the properties of the resulting distances and, from our scheme, we built a monopartametric family of metric between pure quantum states. We proposed a manner of extending these metrics for mixed quantum states and we related them with some previously introduced by D. Petz.