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Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

John H. Selby1,*, David Schmid1,2,3, Elie Wolfe2, Ana Belén Sainz1, Ravi Kunjwal4, and Robert W. Spekkens2

  • 1International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-309 Gdańsk, Poland
  • 2Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5
  • 3Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 4Centre for Quantum Information and Communication, Ecole polytechnique de Bruxelles, CP 165, Université libre de Bruxelles, 1050 Brussels, Belgium

  • *john.h.selby@gmail.com
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Phys. Rev. A 107, 062203 – Published 6 June, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.062203

Abstract

The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all physically possible processes. We here consider the question of how to provide a GPT-like characterization of a particular experimental setup within a given physical theory. We show that the resulting characterization is not generally a GPT in and of itself, rather, it is described by a more general mathematical object that we introduce and term an accessible GPT fragment. We then introduce an equivalence relation, termed cone equivalence, between accessible GPT fragments (and, as a special case, between standard GPTs). We give a number of examples of experimental scenarios that are best described using accessible GPT fragments, and where moreover, cone-equivalence arises naturally. We then prove that an accessible GPT fragment admits of a classical explanation if and only if every other fragment that is cone equivalent to it also admits of a classical explanation. Finally, we leverage this result to prove several fundamental results regarding the experimental requirements for witnessing the failure of generalized noncontextuality. In particular, we prove that neither incompatibility among measurements nor the assumption of freedom of choice is necessary for witnessing failures of generalized noncontextuality, and moreover, that such failures can be witnessed even when using arbitrarily inefficient detectors.

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Physics Subject Headings (PhySH)

See Also

Contextuality without Incompatibility

John H. Selby, David Schmid, Elie Wolfe, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens
Phys. Rev. Lett. 130, 230201 (2023)

Article Text

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Outline

Information

Phys. Rev. A 107, 062203– Published 6 June, 2023
  • Received 16 February 2022
  • Revised 10 February 2023
  • Accepted 21 April 2023
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