Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

ANA MAJTEY; PEDRO W. LAMBERTI; DOMINGO PRATO

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

The American Physical Society

Año: 2005 vol. 72 p. 523101 - 523106

1050-2947

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence JSDbetween probability distributions. The JSD has several interesting properties. It arises in information theoryand, unlike the Kullback-Leibler divergence, it is symmetric, always well-defined, and bounded. We show that the quantum JSD shares with the relative entropy most of the physically relevant properties, in particular thoserequired for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.Dbetween probability distributions. The JSD has several interesting properties. It arises in information theoryand, unlike the Kullback-Leibler divergence, it is symmetric, always well-defined, and bounded. We show that the quantum JSD shares with the relative entropy most of the physically relevant properties, in particular thoserequired for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.