Eur. Phys. J. D 32, 413-419 (2005)
https://doi.org/10.1140/epjd/e2005-00005-1

Wootters' distance revisited: a new distinguishability criterium

¹ Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
² Instituto de Física (IFLP), Universidad Nacional de La Plata and CONICET, C.C. 727, La Plata 1900, Argentina

Corresponding author: ^a lamberti@fis.uncor.edu

Received: 3 August 2004
Revised: 11 November 2004
Published online: 25 January 2005

Abstract

The notion of distinguishability between quantum states has shown to be fundamental in the frame of quantum information theory. In this paper we present a new distinguishability criterium by using a information theoretic quantity: the Jensen-Shannon divergence (JSD). This quantity has several interesting properties, both from a conceptual and a formal point of view. Previous to define this distinguishability criterium, we review some of the most frequently used distances defined over quantum mechanics' Hilbert space. In this point our main claim is that the JSD can be taken as a unifying distance between quantum states.