Extreme commutative quantum observables are sharp



: Heinosaari T, Pellonpaa JP

Publisher: IOP PUBLISHING LTD

: 2011

: Journal of Physics A: Mathematical and Theoretical

: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

: J PHYS A-MATH THEOR

: ARTN 315303

: 31

: 44

: 31

: 4

: 978-0-521-19583-6

: 1751-8113

DOI: https://doi.org/10.1088/1751-8113/44/31/315303

: https://arxiv.org/abs/1106.4295


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.



Last updated on 2024-26-11 at 20:09