Quantum relative entropy

Summary

The quantum relative entropy $S(\rho \| \sigma)$ is a measure of how distinguishable a quantum state $\rho$ is from a quantum state $\sigma$. It is the quantum analogue of the Kullback–Leibler divergence and reduces to it for commuting states. It is nonnegative, vanishes only when $\rho = \sigma$, and cannot increase under quantum channels. Most entropic quantities of quantum information, such as von Neumann entropy and mutual information, are special cases of it.