Metric character of the quantum Jensen-Shannon divergence

P. W. Lamberti, A. P. Majtey, A. Borras, M. Casas, and A. Plastino

Phys. Rev. A 77, 052311 – Published 9 May 2008

Abstract

In a recent paper, the generalization of the Jensen-Shannon divergence in the context of quantum theory has been studied [Majtey et al., Phys. Rev. A 72, 052310 (2005)]. This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of a numerical procedure for mixed states, that its square root verifies the triangle inequality.

Received 10 January 2008

DOI:https://doi.org/10.1103/PhysRevA.77.052311

Authors & Affiliations

P. W. Lamberti¹, A. P. Majtey², A. Borras², M. Casas², and A. Plastino³

¹Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, and CONICET, C.C. 727, La Plata 1900, Argentina
²Departament de Física and IFISC, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
³Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, C.C. 727, La Plata 1900, Argentina

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Issue

Vol. 77, Iss. 5 — May 2008

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