In a recent paper, we have studied a generalization of the Jensen–Shannon divergence (JSD) (Physica A 329 (2003) 81). This generalization was made in the context of Tsallis’ statistical mechanics. The present work is devoted to an investigation of the metric character of the JSD generalization.

We discuss the paradigmatic bipartite spin-12 system having the probabilities (1+3x)/4 of being in the Einstein–Podolsky–Rosen fully entangled state |Ψ−〉≡1/2(|↑〉A|↓〉B−|↓〉A|↑〉B) and 3(1−x)/4 of being orthogonal. This system is known to be separable if and only if...