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Otfried Gühne

Universität Siegen, Germany, otfried.guehne@uni-siegen.de

Proof of the Peres conjecture for contextuality

(joint work with Zhen-Peng Xu and Jing-Ling Chen)

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 compatible observables. 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 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. With this approach, we find the provably minimal GHZ-type proof. Based on our results, we show that the Kochen-Specker set with 18 vectors from Cabello et al. [1] is the minimal set for any dimension, verifying a long-standing conjecture by Peres. Our results allow to identify minimal contextuality scenarios and to study their usefulness for information processing.

[1] A. Cabello, J. Estebaranz, and G. García-Alcaine, Phys. Lett. A 212, 183 (1996).