Covariant positive operator valued measures and instruments: an overview.

Covariance with respect to some symmetry group representation is a natural strong request imposed upon the whole set of measurements that can be performed on a quantum system, and, as such, it greatly simplifies their mathematical description. In this seminar, we present some general structure theorems for covariant positive operator valued measures and instruments, and apply them to two classes of measurements arising in quantum physics: the position and momentum measurements for a quantum particle, and the phase observables for the photon.