= Entanglement-assisted statistical singlet verification
{title2=$\Omega=P_s+(I-P_s)/3$}
Choose a shared random axis uniformly from $x,y,z$, perform its <entanglement-assisted nondemolition parity measurement> with one <Bell pair>, and accept the anticorrelated parity. The <spin singlet state> always passes unchanged. The averaged acceptance operator is $\Omega=\sum_j(I-\sigma_j\otimes\sigma_j)/6=P_s+(I-P_s)/3$, so an orthogonal triplet state passes with probability one third. This is a statistical verifier with a nonzero acceptance gap, rather than an exact single-shot singlet-versus-triplet decision. The <Bell-pair cost of exact nondemolition singlet verification> concerns the stronger zero-error task.
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