A1 Refereed original research article in a scientific journal
Random positive operator valued measures
Authors: Heinosaari T, Jivulescu MA, Nechita I
Publisher: AMER INST PHYSICS
Publication year: 2020
Journal: Journal of Mathematical Physics
Journal name in source: JOURNAL OF MATHEMATICAL PHYSICS
Journal acronym: J MATH PHYS
Volume: 61
Issue: 4
Number of pages: 27
ISSN: 0022-2488
eISSN: 1089-7658
DOI: https://doi.org/10.1063/1.5131028
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/47355507
Abstract
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, starting from the limiting eigenvalue distribution. We derive the large system limit for several quantities of interest in quantum information theory, such as the sharpness, the noise content, and the probability range. Finally, we study different compatibility criteria, and we compare them for generic POVMs.
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, starting from the limiting eigenvalue distribution. We derive the large system limit for several quantities of interest in quantum information theory, such as the sharpness, the noise content, and the probability range. Finally, we study different compatibility criteria, and we compare them for generic POVMs.
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