A1 Refereed original research article in a scientific journal
Optimal covariant quantum measurements
Authors: Haapasalo Erkka, Pellonpää Juha-Pekka
Publisher: IOP PUBLISHING LTD
Publication year: 2021
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 155304
Volume: 54
Issue: 15
Number of pages: 50
ISSN: 1751-8113
eISSN: 1751-8121
DOI: https://doi.org/10.1088/1751-8121/abe752
Web address : https://iopscience.iop.org/article/10.1088/1751-8121/abe752
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/53718746
We discuss symmetric quantum measurements and the associated covariant observables modelled, respectively, as instruments and positive-operator-valued measures. The emphasis of this work are the optimality properties of the measurements, namely, extremality, informational completeness, and the rank-1 property which contrast the complementary class of (rank-1) projection-valued measures. The first half of this work concentrates solely on finite-outcome measurements symmetric w.r.t. finite groups where we derive exhaustive characterizations for the pointwise Kraus-operators of covariant instruments and necessary and sufficient extremality conditions using these Kraus-operators. We motivate the use of covariance methods by showing that observables covariant with respect to symmetric groups contain a family of representatives from both of the complementary optimality classes of observables and show that even a slight deviation from a rank-1 projection-valued measure can yield an extreme informationally complete rank-1 observable. The latter half of this work derives similar results for continuous measurements in (possibly) infinite dimensions. As an example we study covariant phase space instruments, their structure, and extremality properties.
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