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arXiv:quant-ph/0603168 · Journal of Mathematical Physics

Extremal covariant measurements

Giulio Chiribella, Giacomo Mauro D’Ariano

Published Sep 1, 2006• 14 citations
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Abstract

We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is generally nontransitive. In this case the POVM density is made of multiple orbits of positive operators, and, in the case of extremal measurements, we provide a bound for the number of orbits and for the rank of POVM elements. Two relevant applications are considered, concerning state discrimination with mutually unbiased bases and the maximization of the mutual information.

DOI
10.1063/1.2349481

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