Weighted-SRM optimality with a no-change hypothesis

Establish whether the weighted square-root measurement is asymptotically optimal for the augmented quantum change-interval ensembles that include a no-change hypothesis with fixed prior π₀ and retain the stated conditional prior over anomalous intervals.

Background

The paper analyzes the optimal joint Bayes success probability after adding a no-change hypothesis with fixed prior π₀. It proves that the limiting optimum is π₀+(1−π₀)L, where L is the corresponding conditional localization limit.

The augmented ensemble is nonuniform because the no-change state has a separate fixed prior while anomalous intervals share the remaining prior mass. Although the paper discusses square-root measurements for the conditional anomalous ensembles, it does not establish asymptotic optimality of the appropriately weighted square-root measurement for this full augmented discrimination problem.