Proof of the Peres Conjecture for Contextuality

Zhen-Peng Xu, Jing-Ling Chen, and Otfried Gühne
Phys. Rev. Lett. 124, 230401 – Published 9 June 2020
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Abstract

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics cannot be reconciled with classical models that are noncontextual for ideal measurements. The first explicit derivation by Kochen and Specker was rather complex, but considerable simplifications have been achieved thereafter. We propose a systematic approach to find minimal Hardy-type and Greenberger-Horne-Zeilinger-type (GHZ-type) proofs of the Kochen-Specker theorem, these are characterized by the fact that the predictions of classical models are opposite to the predictions of quantum mechanics. Based on our results, we show that the Kochen-Specker set with 18 vectors from Cabello et al. [Phys. Lett. A 212, 183 (1996)] is the minimal set for any dimension, verifying a longstanding conjecture by Peres. Our results allow to identify minimal contextuality scenarios and to study their usefulness for information processing.

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  • Received 20 February 2020
  • Revised 24 April 2020
  • Accepted 15 May 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.230401

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Zhen-Peng Xu1,2,*, Jing-Ling Chen2,†, and Otfried Gühne1,‡

  • 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
  • 2Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, China

  • *Zhen-Peng.Xu@uni-siegen.de
  • chenjl@nankai.edu.cn
  • otfried.guehne@uni-siegen.de

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Issue

Vol. 124, Iss. 23 — 12 June 2020

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