Joint Measurability of Generalized Measurements Implies Classicality

Roope Uola, Tobias Moroder, and Otfried Gühne
Phys. Rev. Lett. 113, 160403 – Published 14 October 2014

Abstract

The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and is responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements, quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether the already show quantum features. We prove that a set of generalized measurements which does not satisfy the notion of joint measurability is nonclassical, as it can be used for the task of quantum steering. This shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. Moreover, the equivalence allows one to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.

  • Figure
  • Received 9 July 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.160403

© 2014 American Physical Society

Authors & Affiliations

Roope Uola, Tobias Moroder, and Otfried Gühne

  • Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Strasse 3, 57068 Siegen, Germany

See Also

Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality

Marco Túlio Quintino, Tamás Vértesi, and Nicolas Brunner
Phys. Rev. Lett. 113, 160402 (2014)

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Issue

Vol. 113, Iss. 16 — 17 October 2014

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