Error rates of Belavkin weighted quantum measurements and a converse to Holevo’s asymptotic optimality Theorem
نویسنده
چکیده
We compare several instances of pure-state Belavkin weighted square-root measurements from the standpoint of minimum-error discrimination of quantum states. The quadratically weighted measurement is proven superior to the so-called “pretty good measurement” (PGM) in a number of respects: 1. Holevo’s quadratic weighting unconditionally outperforms the PGM in the case of twostate ensembles, with equality only in trivial cases. 2. A converse of a theorem of Holevo is proven, showing that a weighted measurement is asymptotically-optimal only if it is quadratically weighted. Counter-examples for three states are constructed. The cube-weighted measurement of Ballester, Wehner, and Winter is also considered. Sufficient optimality conditions for various weights are compared. [email protected], where X=post, Y=Harvard, Z=edu
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