For any quantum ensemble and any positive score function, the optimal expected gain is no larger than the square root of the gain of the generalized pretty good measurement, implying a two-fold mean-square-error bound in Bayesian estimation.
Optimal distinction of non-ortho gonal quantum signals
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Near-optimal performance of square-root measurement for general score functions and quantum ensembles
For any quantum ensemble and any positive score function, the optimal expected gain is no larger than the square root of the gain of the generalized pretty good measurement, implying a two-fold mean-square-error bound in Bayesian estimation.