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GENERALIZED COHERENT STATES AND EXTREMAL POSITIVE OPERATOR VALUED MEASURES

Teiko Heinosaari, Juha-Pekka Pellonpää

Published Aug 17, 2016• 7 citations
OpenAlex

Abstract

We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. POVMs describe quantum observables and, similar to quantum states, quantum observables can also 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 those related to number states are not extremal.

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We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. POVMs describe quantum observables and, similar to quantum states, quantum observables can also 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 those related to number states are not extremal.
We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. POVMs describe quantum observables and, similar to quantum states, quantum observables can also 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 those related to number states are not extremal. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Coherent states: mathematical and physical aspects'.
Measurements on quantum channels are described by so-called process positive operator valued measures, or process POVMs. We study implementing schemes of extremal process POVMs. As it turns out, the corresponding measurement must satisfy certain extremality property, which is stronger than the usual extremality given by the convex structure. This property motivates the introduction and investigation of the A-convex structure of POVMs, which generalizes both the usual convex and C*-convex structures. We show that extremal points and faces of the set of process POVMs are closely related to A-extremal points and A-faces of POVMs, for a certain subalgebra A. We also give a characterization of A-extremal and A-pure POVMs.