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

2009/03/31 by Jon Tyson, Jon E. Tyson · 2 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.79.032343

published as Phys. Rev. A 79, 032343 (2009)

openalex publication_date 2009/03/31 · arxiv created 2009/07/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Estimates of non-optimality of quantum measurements and a simple iterative method for computing optimal measurements
• Multiparty data hiding of quantum information
• Statistical decision theory for quantum systems
• Optimal single-copy measurement for the hidden-subgroup problem
• State Discrimination With Post-Measurement Information
• Minimum-error discrimination of quantum states: New bounds and comparison

Cited by

• Qubit state discrimination
• Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on maximum overlap using directional iterates

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