A Kochen-Specker inequality from a SIC

TL;DR

This paper presents a new state-independent Kochen-Specker inequality derived from a symmetric informationally complete measurement and mutually unbiased bases, highlighting quantum contextuality in three dimensions.

Contribution

It introduces a novel Kochen-Specker inequality based on 21 rays forming a SIC and four MUBs, expanding previous proofs with a different geometric configuration.

Findings

The inequality is violated by quantum mechanics, confirming contextuality.

The proof uses a configuration of 21 rays and four MUBs.

It provides a new approach to state-independent contextuality proofs.

Abstract

Yu and Oh [1] have given a state independent proof of the Kochen-Specker theorem in three dimensions using only 13 rays. The proof consists of showing that a non-contextual hidden variable theory necessarily leads to an inequality that is violated by quantum mechanics. We give a similar proof making use of 21 rays that constitute a SIC and four Mutually Unbiased Bases.