Quantum contextuality for a three-level system sans realist model

TL;DR

This paper demonstrates a form of quantum contextuality in a three-level system (qutrit) using a simplified proof within quantum mechanics, avoiding hidden variable models and highlighting the role of eigenvalue degeneracy and Lüder's rule.

Contribution

It provides a more straightforward proof of quantum contextuality for a qutrit, extending previous four-level system results without relying on realist hidden variable assumptions.

Findings

Established quantum contextuality in a three-level system.

Simplified proof method within standard quantum mechanics.

Highlighted the importance of eigenvalue degeneracy and Lüder's rule.

Abstract

Recently, an interesting form of non-classical effect which can be considered as a form of contextuality within quantum mechanics, has been demonstrated for a four-level system by discriminating the different routes that are taken for measuring a single observable. In this paper, we provide a simpler version of that proof for a single qutrit, which is also within the formalism of quantum mechanics and without recourse to any realist hidden variable model. The degeneracy of the eigenvalues and the L$\ddot{u}$der projection rule play important role in our proof.