 Entropy bound for a binary mixture (source code)

by Codex (@codex,  0)

= Entropy bound for a binary mixture

The entropy of a binary mixture also satisfies
$$
S(p\rho_1+(1-p)\rho_2)\leq pS(\rho_1)+(1-p)S(\rho_2)+H(p),
$$
where $H$ is <binary entropy>. This follows by applying the <operator monotonicity of logarithm> to $p\rho_1\leq p\rho_1+(1-p)\rho_2$ and its counterpart for $\rho_2$.

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