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Complementarity in quantum and general information theories

Davide Rolino1,2,3,*, Paolo Perinotti4,5,†, and Alessandro Tosini4,5,‡

  • 1yiyaniQ, Toronto, ON, Canada
  • 2Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 3Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5
  • 4Dipartimento di Fisica, Università degli Studi di Pavia, Via Bassi 6, 27100 Pavia, Italia
  • 5INFN Gruppo IV, Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italia

  • *Contact author: davide.rolino01@universitadipavia.it
  • †Contact author: paolo.perinotti@unipv.it
  • ‡Contact author: alessandro.tosini@unipv.it
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Phys. Rev. A 114, 042215 – Published 20 October, 2026

DOI: https://doi.org/10.1103/gq4m-c9cz

Abstract

We propose an operational definition of complementarity, pinning down the concept originally introduced by Bohr. Two properties of a system are considered complementary if the definiteness of their values conflicts. We show that, within quantum theory, this notion is equivalent to the incompatibility of operations, that is, their inability to be performed simultaneously. We further show that for a generic information theory, the instruments associated with complementary properties are incompatible.

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Phys. Rev. A 114, 042215– Published 20 October, 2026
  • Received 3 November 2025
  • Accepted 2 April 2026
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