Graphical Non-contextual Inequalities for Qutrit Systems

TL;DR

This paper introduces a hyper-graph based method to derive non-contextual inequalities for qutrit systems, aiding in understanding quantum contextuality and simplifying related proofs.

Contribution

It presents a new, extensible hyper-graph framework for constructing non-contextual inequalities in qutrit systems, advancing analytical approaches in quantum contextuality.

Findings

Developed a general hyper-graph based method for inequalities

Discussed several families of non-contextual inequalities

Simplified state-independent proofs of quantum contextuality

Abstract

One of the interesting topics in quantum contextuality is the construction for various non-contextual inequalities. By introducing a new structure called hyper-graph, we present a general method, which seems to be analytic and extensible, to derive the non-contextual inequalities for the qutrit systems. Based on this, several typical families of non-contextual inequalities are discussed. And our approach may also help us to simplify some state-independent proofs for quantum contextuality in one of our recent works.