Uniqueness of Noncontextual Models for Stabilizer Subtheories

David Schmid, Haoxing Du, John H. Selby, and Matthew F. Pusey
Phys. Rev. Lett. 129, 120403 – Published 14 September 2022
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Abstract

We give a complete characterization of the (non)classicality of all stabilizer subtheories. First, we prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in all odd dimensions, namely Gross’s discrete Wigner function. This representation is equivalent to Spekkens’ epistemically restricted toy theory, which is consequently singled out as the unique noncontextual ontological model for the stabilizer subtheory. Strikingly, the principle of noncontextuality is powerful enough (at least in this setting) to single out one particular classical realist interpretation. Our result explains the practical utility of Gross’s representation by showing that (in the setting of the stabilizer subtheory) negativity in this particular representation implies generalized contextuality. Since negativity of this particular representation is a necessary resource for universal quantum computation in the state injection model, it follows that generalized contextuality is also a necessary resource for universal quantum computation in this model. In all even dimensions, we prove that there does not exist any nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory, and, hence, that the stabilizer subtheory is contextual in all even dimensions.

  • Received 2 March 2021
  • Revised 17 April 2022
  • Accepted 29 June 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.120403

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

David Schmid1,2,3, Haoxing Du4, John H. Selby3, and Matthew F. Pusey5

  • 1Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada, N2L 2Y5
  • 2Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • 3International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland
  • 4Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
  • 5Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom

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Issue

Vol. 129, Iss. 12 — 16 September 2022

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