Work

Minimal ring extensions of the integers exhibiting Kochen–Specker contextuality

Year: 2025

Type: article

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 [Formula: see text] symmetric matrices ([Formula: see text]) admits no morphism to a nonzero commutative ring, which we view as an “algebraic hidden state”. For [Formula: see text], the minimal such ring is shown to be [Formula: see text], while for [Formula: see text] the minimal subring is [Formula: see text] itself. The proofs rely on the construction of new sets of integer vectors in dimensions 3 and 6 that have no Kochen–Specker coloring.

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s0219498825420174

Authors: Ida Cortez, Camilo Morales, Manuel Reyes

Institutions: Bowdoin College, Harvey Mudd College, University of California, Irvine

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Maine Space Grant Consortium, University of California, Irvine

Award: Geometric Insights in Noncommutative Algebra