Generalized Coherent States and Extremal Positive Operator Valued Measures

TL;DR

This paper explores the relationship between POVMs and generalized coherent states, providing a characterization of extremal POVMs and analyzing specific cases like covariant phase space observables.

Contribution

It introduces a formalism linking POVMs with generalized coherent states and characterizes extremal POVMs, including covariant phase space observables.

Findings

Covariant phase space observables related to squeezed states are extremal.

Covariant phase space observables related to number states are not extremal.

The formalism offers a new way to analyze quantum measurements.

Abstract

We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. Positive operator valued measures describe quantum observables and, similarly to quantum states, also quantum observables can be mixed. We show how the formalism of generalized coherent states leads to a useful characterization of extremal POVMs. We prove that covariant phase space observables related to squeezed states are extremal, while the ones related to number states are not extremal.