 Weak monotonicity of quantum entropy (source code)

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= Weak monotonicity of quantum entropy
{title2=$S(AC)+S(BC)\geq S(A)+S(B)$}

Every tripartite <density operator> satisfies $S(AC)+S(BC)\geq S(A)+S(B)$. Purify to $ABCD$ and apply <Strong subadditivity of Von Neumann entropy> to $ACD$, conditioned on $A$. The <Schmidt decomposition> gives $S(AD)=S(BC)$ and $S(ACD)=S(B)$, proving the inequality. The original tripartite state need not be pure.

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