On a quantum version of Shannon's conditional entropy

Abstract

In this article we propose a quantum version of Shannon's conditional entropy. Given two density matrices $\rho$ and $\sigma$ on a finite dimensional Hilbert space and with $S(ρ)=-\trρ\lnρ$ being the usual von Neumann entropy, this quantity $S(\rho |\sigma )$ is concave in $\rho$ and satisfies $0\le S(\rho |\sigma )\le S(\rho )$, a quantum analogue of Shannon's famous inequality. Thus we view $S(\rho |\sigma )$ as the entropy of $\rho$ conditioned by $\sigma$.

17 pages of latex

Cited by in corpus (1)

• On quantum conditional entropies defined in terms of the $f$-divergences