An Alternative Distance for Hilbert Space

A.P. MAJTEY; A. BORRAS; P.W. LAMBERTI; M. CASAS

Erice

Conferencia; Noise Information & Complexity @ Quantum Scale; 2007

The notion of distance in Hilbert space is relevant in several scenarios. In particular, distances between quantum states play a central role in quantum information theory. We discuss an extension to the realm of quantum mechanics of the Jensen Shannon divergence (JSD) between probability distributions as a measure of distance between quantum states. We show that the quantum JSD shares with the relative entropy most of the physical relevant properties and we relate it to other known quantum distances. As an application to quantum information we generate an entanglement measure and an alternative concept of the so called fidelity.