Exact delayed-query scoring and classical nulls

Measure-and-prepare channels are the entanglement-breaking channel class HorodeckiShorRuskai2003. The bound above is a trusted-input channel statement. It is distinct from an arbitrary classical encoder with a two-state storage bottleneck, although that bottleneck also has the sharp value $3/4$ in the task considered in Psy04-A CheungPsy04A. Neither statement is a universal “classical black-hole” bound.

In particular, if an early quantum resource survives outside the asserted classical cut, then the complete channel must include that resource before Theorem thm:classical can be applied. Entanglement breaking of one selected radiation factor does not establish entanglement breaking of the complete accessible output.