A1 Refereed original research article in a scientific journal
Post-processing minimal joint observables
Authors: Teiko Heinosaari, Yui Kuramochi
Publisher: IOP PUBLISHING LTD
Publication year: 2019
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 065301
Volume: 52
Issue: 6
Number of pages: 22
ISSN: 1751-8113
eISSN: 1751-8121
DOI: https://doi.org/10.1088/1751-8121/aaf7bb
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/39603613
A finite set of quantum observables (positive operator valued measures) is called compatible if these observables are marginals of a some observable, called a joint observable of them. For a given set of compatible observables, their joint observable is in general not unique and it is desirable to take a minimal joint observable in the post-processing order since a less informative observable disturbs the system less. We address the question of the minimality of finite-outcome joint observables and prove that any joint observable is lower bounded by a minimal joint observable in the post-processing order. We also give characterizations of the minimality of a joint observable that can be checked by finite-step algorithms and apply them to the case of non-commuting dichotomic qubit observables.
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