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
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Category:Quantum Information Theory
Category:Handbook of Quantum Information
Category:Entropy

## Last modified:

Sunday, November 12, 2017 - 00:49