A1 Refereed original research article in a scientific journal
Extreme commutative quantum observables are sharp
Authors: Heinosaari T, Pellonpaa JP
Publisher: IOP PUBLISHING LTD
Publication year: 2011
Journal: Journal of Physics A: Mathematical and Theoretical
Journal name in source: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Journal acronym: J PHYS A-MATH THEOR
Article number: ARTN 315303
Number in series: 31
Volume: 44
Issue: 31
Number of pages: 4
ISBN: 978-0-521-19583-6
ISSN: 1751-8113
DOI: https://doi.org/10.1088/1751-8113/44/31/315303
Self-archived copy’s web address: https://arxiv.org/abs/1106.4295
Abstract
It is well known that, in the description of quantum observables, positive operator valued measures (POVMs) generalize projection valued measures (PVMs) and they also turn out be more optimal in many tasks. We show that a commutative POVM is an extreme point in the convex set of all POVMs if and only if it is a PVM. This results implies that non-commutativity is a necessary ingredient to overcome the limitations of PVMs.
It is well known that, in the description of quantum observables, positive operator valued measures (POVMs) generalize projection valued measures (PVMs) and they also turn out be more optimal in many tasks. We show that a commutative POVM is an extreme point in the convex set of all POVMs if and only if it is a PVM. This results implies that non-commutativity is a necessary ingredient to overcome the limitations of PVMs.
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