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An Isaac Newton Institute Workshop

Quantum Statistics - quantum measurements, estimation and related topics

Extremal covariant POVM's

Authors: G. Chiribella (QUIT group, Universita' di Pavia), G. M. D'Ariano (QUIT group, Universita' di Pavia), P. Perinotti (QUIT group, Universita' di Pavia), M. F. Sacchi (QUIT group, Universita' di Pavia)

Abstract

The random choice between two different apparatuses measuring the same physical parameter can be viewed as a convex combination in the space of quantum measurements. In particular, the set of positive operator valued measures (POVM) pertaining to a given parameter is a convex set. The aim of this work is to characterize the extreme points of the set of POVM's which are covariant with respect to a finite dimensional representation of a Lie group. Necessary and sufficient conditions are given, also relating extremality with uniqueness and stability of measurements arising in concrete optimization problems.

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