Quantifying the Incompatibility of Quantum Measurements Relative to a Basis

Georgios Styliaris and Paolo Zanardi
Phys. Rev. Lett. 123, 070401 – Published 12 August 2019
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Abstract

Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability distributions associated with different quantum measurements can be converted into one another by probabilistic postprocessing. The induced preorder over quantum measurements is directly related to multivariate majorization and gives rise to families of monotones, i.e., scalar quantifiers that preserve the ordering. For the case of orthogonal measurement we establish a quantitative connection between incompatibility, quantum coherence and entropic uncertainty relations. We generalize the construction to include arbitrary positive-operator-valued measurements and report complete families of monotones.

  • Received 31 January 2019
  • Revised 25 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.070401

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Georgios Styliaris and Paolo Zanardi

  • Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA

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Issue

Vol. 123, Iss. 7 — 16 August 2019

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