Document Type

Research Article

Publication Title

Communications in Mathematical Physics

Abstract

We study the quantum (C∗) convexity structure of normalized positive operator valued measures (POVMs) on measurable spaces. In particular, it is seen that unlike extreme points under classical convexity, C∗-extreme points of normalized POVMs on countable spaces (in particular for finite sets) are always spectral measures (normalized projection valued measures). More generally it is shown that atomic C∗-extreme points are spectral. A Krein–Milman type theorem for POVMs has also been proved. As an application it is shown that a map on any commutative unital C∗-algebra with countable spectrum (in particular Cn) is C∗-extreme in the set of unital completely positive maps if and only if it is a unital ∗ -homomorphism.

First Page

1235

Last Page

1280

DOI

10.1007/s00220-021-04245-1

Publication Date

12-1-2021

Comments

Open Access, Green

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