Quantum recovery reveals nonprojective advantage in state exclusion

A projective measurement can perfectly exclude a state from a qubit ensemble containing an orthogonal pair. If the same device must also preserve entanglement with a reference, a general readout can achieve a lower exclusion error than any projectively simulable readout, even when both classes allow arbitrary state updates. For such pure-state ensembles at unit efficiency, both readout classes have quadratic error at small recovery. The coefficient is set by balanced Bloch directions for unrestricted readouts and by antipodal pairs for projectively simulable readouts. For projectively simulable instruments the optimal error is linear in the recovery floor. With a common zero-error baseline at unit efficiency, the gap between the two readout classes requires at least three pure probes, or four for a quadratic gap. For five probes we find exactly when the gap survives input-dependent erasure and give a finite-count test at 80% efficiency. The record includes the preprint, Supplemental Material, and a reproducibility archive with scripts and calculated outputs.