Quantum relative entropy

The quantum relative entropy, in analogy with the [[classical relative entropy]] or [[Kullback-Leibler divergence]], is a measure of closeness between two states. It was defined by [[Denis Petz]] as :$D(\backslash rho||\backslash sigma)=Tr\backslash rho(\backslash log\backslash rho-\backslash log\backslash sigma)$ where $\backslash rho$ and $\backslash sigma$ are two density matrices. It has a number of applications including its use in proving [[strong sub-additivity]]. One can also define a [[relative entropy distance]] to some set of states, where one minimises $D(\backslash rho||\backslash sigma)$ over all $\backslash sigma$ from some [[convex set]]. If the convex set is chosen to be the set of [[seperable states]], then the relative entropy distance is an entanglement measure, called the [[relative entropy of entanglement]]. If the set of states are [[product states]], then the relative entropy distance is the [[quantum mutual information]] == See also == * [[Entropy of entanglement]] {{stub}} [[Category:Quantum Information Theory]] [[Category:Handbook of Quantum Information]] [[Category:Entropy]]