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On a quantum version of Shannon's conditional entropy

Robert Schrader
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Abstract

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

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Robert Schrader. 2000-03-14. On a quantum version of Shannon's conditional entropy. https://doi.org/10.1002/1521-3978(200008)48%3A8%3C747%3A%3Aaid-prop747%3E3.0.co%3B2-t

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