Necessary condition for incompatibility of observables in general probabilistic theories

Sergey N. Filippov, Teiko Heinosaari, and Leevi Leppäjärvi
Phys. Rev. A 95, 032127 – Published 22 March 2017

Abstract

We quantify the intrinsic noise content of an observable in a general probabilistic theory and derive a noise content inequality for incompatible observables. We apply the derived inequality to standard quantum theory, the quantum theory of processes, and polytope state spaces. The noise content for positive operator-valued measures takes a particularly simple form and equals the sum of minimal eigenvalues of all the effects. We illustrate our findings with a number of examples including the introduced notion of reverse observables.

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  • Received 7 October 2016

DOI:https://doi.org/10.1103/PhysRevA.95.032127

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
General Physics

Authors & Affiliations

Sergey N. Filippov*

  • Institute of Physics and Technology, Russian Academy of Sciences, Moscow, Russia and Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia

Teiko Heinosaari and Leevi Leppäjärvi

  • Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland

  • *sergey.filippov@phystech.edu
  • teiko.heinosaari@utu.fi
  • leille@utu.fi

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Issue

Vol. 95, Iss. 3 — March 2017

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