= Bell-pair cost of exact nondemolition singlet verification
{c}
{title2=$R\geq4$}
Exact singlet verification accepts the <spin singlet state> with certainty, rejects every orthogonal state, and preserves the singlet on acceptance. Each nonzero accepting <Kraus operator> is then a scalar multiple of the singlet projector, whose <operator Schmidt rank> is four. The <local Kraus rank bound from an entangled resource> excludes a single shared <Bell pair>, which has <Schmidt rank> two. Two shared <Bell pairs> suffice by a <Bell-state nondemolition measurement> followed by reporting whether its label is the singlet. This protocol may disturb triplet coherence. The rank bound concerns the resource <Schmidt rank>, and is not an entropy lower bound of two bits for arbitrary resource states.
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