 Quantum relative entropy

The quantum relative entropy is $D(\rho \Vert \sigma )=\mathrm{Tr}[\rho (\log \rho -\log \sigma )]$ when the support of $\rho$ lies in that of $\sigma$.

Quantum relative entropy is a concept from quantum information theory that quantifies the difference between two quantum states in terms of information theory. It is a generalization of the classical relative entropy (or Kullback-Leibler divergence) to the quantum domain.