Divergences in the 2-qubits space: Werner and thermal states

Abstract

We revisit the notion of using divergences, or relative-entropies, as measures of the distance between two mixed states, with special emphasis on power-law entropies. We analyze the Csisz´ar and Bregmantype q-divergences with reference to i) Werner states, and ii) thermal states obtained using a one-dimensional Heisenberg two-spin chain with a magnetic field B along the z-axis. In both cases, we find that the q-Jensen-Shannon divergence enlarges the range of permissible powerlaw exponents, as compared to results of previous literature. It is also shown that this divergence-measure serves as a good indicator for critical phenomena in the Heisenberg model.