pith. sign in

arxiv: 0907.1884 · v1 · submitted 2009-07-10 · 🪐 quant-ph

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

classification 🪐 quant-ph
keywords weightedmeasurementholevobelavkinconversemeasurementsonlyoptimality
0
0 comments X
read the original 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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.