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arXiv · 0907.1884

Error rates of Belavkin weighted quantum measurements and a converse to Holevo's asymptotic optimality theorem

Jon Tyson
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Abstract

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 two-state 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. Counterexamples 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.

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Jon Tyson. 2009-07-10. Error rates of Belavkin weighted quantum measurements and a converse to Holevo's asymptotic optimality theorem. https://doi.org/10.1103/physreva.79.032343

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