A1 Refereed original research article in a scientific journal
Quantum measurement incompatibility in subspaces
Authors: Uola Roope, Kraft Tristan, Designolle Sebastien, Miklin Nikolai, Tavakoli Armin, Pellonpää Juha-Pekka, Guhne Otfried, Brunner Nicolas
Publisher: AMER PHYSICAL SOC
Publication year: 2021
Journal: Physical Review A
Journal name in source: PHYSICAL REVIEW A
Journal acronym: PHYS REV A
Article number: ARTN 022203
Volume: 103
Issue: 2
Number of pages: 10
ISSN: 2469-9926
eISSN: 2469-9934
DOI: https://doi.org/10.1103/PhysRevA.103.022203
Web address : https://doi.org/10.1103/PhysRevA.103.022203
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/53433630
We consider the question of characterizing the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility-measurements that become compatible in every subspace, (ii) fully compressible incompatibility-measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility-measurements that are compatible in some subspace and incompatible in another. For each class, we discuss explicit examples. Finally, we present some applications of these ideas. First, we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second, we highlight the implications of our results for tests of quantum steering.
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