CHSH inequality always holds in bipartite qutrits with spin-1 observables

TL;DR

This paper proves that in bipartite qutrit systems with spin-1 observables, the CHSH inequality always holds, confirming a conjecture and showing no violation occurs regardless of the state being pure or mixed.

Contribution

It establishes that all bipartite states of two qutrits satisfy the CHSH inequality under spin-1 measurements, extending previous conjectures.

Findings

CHSH inequality always holds for bipartite qutrits with spin-1 observables

No violation of CHSH inequality for any bipartite qutrit state

Confirms a conjecture about non-violation in mixed and pure states

Abstract

We resolve a conjecture of Hanotel and Loubenets concerning CHSH inequality in bipartite qutrits. It states that nonseparable pure states of two qutrits do not violate the CHSH inequality when each party is restricted to spin-1 observables. We prove a stronger result that \emph{all} bipartite states on $\mathbb{C}^3 \otimes \mathbb{C}^3$ satisfy the CHSH inequality under spin-1 measurements, regardless of whether the state is pure or mixed.