### 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.

### Related Links

- www.qubit.it - Website of QUIT group
- http://arxiv.org/pdf/quant-ph/0406237 - Extremal covariant POVM's
- http://arxiv.org/pdf/quant-ph/0403083 - Covariant quantum measurements that maximize the likelihood
- http://arxiv.org/pdf/quant-ph/0405095 - Efficient use of quantum resources in the transmission of a reference frame