Efficient measurement for symmetry-adapted retained states

Construct an efficient quantum measurement that accesses the distinguishing power retained by the label-and-Specht output, or by the Specht register alone, after symmetry-adapted Schur processing of the full graph-register encoding.

Background

The Schur transform can be implemented efficiently and produces reduced states with near-perfect statistical distinguishability, even though weak Schur labels alone have vanishing power. The paper identifies two measurement targets: a measurement on the retained label and Specht register that may depend on the label, and a single label-independent measurement on the common Specht register. Whether either target can be implemented efficiently is left unresolved.