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Quantum Simulation Entanglement Theory Quantum Correlations Quantum State Preparation Representation Quantum Foundations

Minimal ring extensions of the integers exhibiting Kochen-Specker contextuality

arXiv

Authors: Ida Cortez, Camilo Morales, Manuel Reyes

Year

2022

Paper ID

6605

Status

Preprint

Abstract Read

~2 min

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Abstract

This paper is a contribution to the algebraic study of contextuality in quantum theory. As an algebraic analogue of Kochen and Specker's no-hidden-variables result, we investigate rational subrings over which the partial ring of d times d symmetric matrices $d geq 3$ admits no morphism to a commutative ring, which we view as an "algebraic hidden state." For d = 3, the minimal such ring is shown to be mathbb{Z}[1/6], while for d geq 6 the minimal subring is mathbb{Z} itself. The proofs rely on the construction of new sets of integer vectors in dimensions 3 and 6 that have no Kochen-Specker coloring.

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This paper is a contribution to the algebraic study of contextuality in quantum theory.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2211.13216 [2] arXiv https://arxiv.org/abs/2211.13216 [3] Publisher https://arxiv.org/abs/2211.13216

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