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Entanglement and Superposition Are Equivalent Concepts in Any Physical Theory

Guillaume Aubrun, Ludovico Lami, Carlos Palazuelos, and Martin Plávala
Phys. Rev. Lett. 128, 160402 – Published 22 April 2022
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Abstract

We prove that given any two general probabilistic theories (GPTs) the following are equivalent: (i) each theory is nonclassical, meaning that neither of their state spaces is a simplex; (ii) each theory satisfies a strong notion of incompatibility equivalent to the existence of “superpositions”; and (iii) the two theories are entangleable, in the sense that their composite exhibits either entangled states or entangled measurements. Intuitively, in the post-quantum GPT setting, a superposition is a set of two binary ensembles of states that are unambiguously distinguishable if the ensemble is revealed before the measurement has occurred, but not if it is revealed after. This notion is important because we show that, just like in quantum theory, superposition in the form of strong incompatibility is sufficient to realize the Bennett-Brassard 1984 protocol for secret key distribution.

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  • Received 20 September 2021
  • Revised 7 December 2021
  • Accepted 9 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.160402

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Guillaume Aubrun1,*, Ludovico Lami2,†, Carlos Palazuelos3,4,‡, and Martin Plávala5,§

  • 1Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne CEDEX, France
  • 2Institute of Theoretical Physics and IQST, Universität Ulm, Albert-Einstein-Allee, 11D-89069 Ulm, Germany
  • 3Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Plaza de Ciencias s/n, 28040 Madrid, Spain,
  • 4Instituto de Ciencias Matemáticas, c/ Nicolás Cabrera, 13-15, 28049 Madrid, Spain
  • 5Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany

  • *aubrun@math.univ-lyon1.fr
  • ludovico.lami@gmail.com
  • carlospalazuelos@mat.ucm.es
  • §martin.plavala@uni-siegen.de

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Issue

Vol. 128, Iss. 16 — 22 April 2022

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