Optimal single-shot strategies for discrimination of quantum measurements

Michal Sedlák and Mário Ziman
Phys. Rev. A 90, 052312 – Published 10 November 2014

Abstract

We study discrimination of m quantum measurements in the scenario when the unknown measurement with n outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably mn. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific quantum states. In particular, the optimal protocol for discrimination of projective qubit measurements with fixed failure rate (exploiting maximally entangled test state) is described. While minimum-error discrimination of two projective qubit measurements can be realized without any need of entanglement, we show that discrimination of three projective qubit measurements requires a bipartite probe state. Moreover, when the measurements are not projective, the non-maximally entangled test states can outperform the maximally entangled ones. Finally, we rephrase the unambiguous discrimination of measurements as quantum key distribution protocol.

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  • Received 4 August 2014

DOI:https://doi.org/10.1103/PhysRevA.90.052312

©2014 American Physical Society

Authors & Affiliations

Michal Sedlák1,2 and Mário Ziman2,3

  • 1Department of Optics, Palacký University, 17. listopadu 1192/12, CZ-771 46 Olomouc, Czech Republic
  • 2Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11 Bratislava, Slovakia
  • 3Faculty of Informatics, Masaryk University, Botanická 68a, 60200 Brno, Czech Republic

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Vol. 90, Iss. 5 — November 2014

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