= Entropy bound from overlap with a pure state
{title2=$S(\sigma)\leq h(t)+(1-t)\log_2(m-1)$}
If a <density operator> $\sigma$ on an $m\geq2$ dimensional <Hilbert space> has overlap $t=\langle\psi|\sigma|\psi\rangle$ with a fixed <pure state>, then $S(\sigma)\leq h(t)+(1-t)\log_2(m-1)$. Dephase in a basis containing $|\psi\rangle$ and apply the <entropy bound with one prescribed probability>. The abstract state bound is attained by $\sigma=t|\psi\rangle\langle\psi|+(1-t)(I-|\psi\rangle\langle\psi|)/(m-1)$.
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