On a quantum version of Shannon's conditional entropy
R. Schrader, Technische Univ. Berlin (Germany). Sonderforschungsbereich 288 -Differentialgeometrie und Quantenphysik · OpenGrey (Institut de l'Information Scientifique et Technique) · 2000
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 $S(\\rho)=-\\tr\\rho\\ln\\rho$ 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 $\\sigma$.