A1 Refereed original research article in a scientific journal
Amount of quantum coherence needed for measurement incompatibility
Authors: Kiukas Jukka, McNulty Daniel, Pellonpää Juha-Pekka
Publisher: AMER PHYSICAL SOC
Publication year: 2022
Journal: Physical Review A
Journal name in source: PHYSICAL REVIEW A
Journal acronym: PHYS REV A
Article number: 012205
Volume: 105
Issue: 1
Number of pages: 18
ISSN: 2469-9926
eISSN: 2469-9934
DOI: https://doi.org/10.1103/PhysRevA.105.012205
Web address : https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.012205
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/174767829
A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to the diagonal elements of any observable jointly measurable with it, leading to a general criterion for the coherence needed for incompatibility. Specializing to the case where the second observable is incoherent (diagonal), we develop a concrete method for solving incompatibility problems, tractable even in large systems by analytical bounds, without resorting to numerical optimization. We verify the consistency of our method by a quick proof of the known noise bound for mutually unbiased bases, and apply it to study emergent classicality in the spin-boson model of an N-qubit open quantum system. Finally, we formulate our theory in an operational resource-theoretic setting involving "genuinely incoherent operations" used previously in the literature, and show that if the coherence is insufficient to sustain incompatibility, the associated joint measurements have sequential implementations via incoherent instruments.
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