A1 Refereed original research article in a scientific journal
Effective methods for constructing extreme quantum observables
Authors: Haapasalo E, Pellonpää JP
Publisher: IOP PUBLISHING LTD
Publication year: 2020
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 245301
Volume: 53
Issue: 24
Number of pages: 14
ISSN: 1751-8113
eISSN: 1751-8121
DOI: https://doi.org/10.1088/1751-8121/ab8d52
Web address : https://iopscience.iop.org/article/10.1088/1751-8121/ab8d52
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/47967023
We study extreme points of the set of finite-outcome positive-operator-valued measures (POVMs) on finite-dimensional Hilbert spaces and particularly the possible ranks of the effects of an extreme POVM. We give results discussing ways of deducing new rank combinations of extreme POVMs from rank combinations of known extreme POVMs and, using these results, show ways to characterize rank combinations of extreme POVMs in low dimensions. We show that, when a rank combination together with a given dimension of the Hilbert space solve a particular packing problem, there is an extreme POVM on the Hilbert space with the given ranks. This geometric method is particularly effective for constructing extreme POVMs with desired rank combinations.
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