Quantum q-divergence

The quantum q-divergence is the nonadditive relative entropy associated with the Tsallis entropy indexed by q. Here, its basic properties including the q-deformation and quantum-group structure, convexity and monotonicity are summarized. Then, it is applied to measuring the degree of state purification. It is shown that the quantum q-divergence is always well defined if the entropic index, q, is in the range (0,1), whereas the ordinary quantum relative entropy is singular when the reference state is a pure state. Thus, the additive limit, q→1−0, does not exist, in general.