On constructing informationally complete covariant positive operator-valued measures

TL;DR

This paper investigates covariant positive operator-valued measures generated by group representations, proving their informational completeness and illustrating with coherent states, advancing quantum measurement theory.

Contribution

It demonstrates that measures generated by group orbits are informationally complete and characterizes their structure using contractions and unitary operators.

Findings

Integration over these measures yields contractions related to the representation.

Measures are proven to be informationally complete.

Illustrated with coherent states density measures.

Abstract

We study positive operator-valued measures generated by orbits of projective unitary representations of locally compact Abelian groups. It is shown that integration over such a measure defines a family of contractions being multiples of unitary operators from the representation. Using this fact it is proved that the measures are informationally complete. The obtained results are illustrated for the measure with density taking values in the set of coherent states.