Witness acceptance operator
= Witness acceptance operator
{title2=$F=J^\dagger U^\dagger\Pi UJ$}
For <quantum witness> embedding $J$, verifier unitary $U$ and accepting projector $\Pi$, the <witness acceptance operator> is the positive contraction $F=J^\dagger U^\dagger\Pi UJ$. The maximum acceptance over normalized <quantum witnesses> is $\lambda_{\max}(F)$ by the <Rayleigh quotient>. Restricting to basis <quantum witnesses> only tests its diagonal entries and need not find that maximum.