Beating the Clauser-Horne-Shimony-Holt and the Svetlichny games with Optimal States

TL;DR

This paper identifies optimal quantum states that maximize nonlocality in Svetlichny and CHSH games, demonstrating their robustness against noise and their relation to classical errors in quantum experiments.

Contribution

It introduces maximally nonlocal mixed states (MNMS) for two- and three-qubit systems, linking their nonlocality to linear entropy and noise tolerance.

Findings

MNMS are the most noise-tolerant states for these games.

Nonlocality ceases at specific linear entropy thresholds.

MNMS relate to classical errors in state preparation.

Abstract

We study the relation between the maximal violation of Svetlichny's inequality and the mixedness of quantum states and obtain the optimal state (i.e., maximally nonlocal mixed states, or MNMS, for each value of linear entropy) to beat the Clauser-Horne-Shimony-Holt and the Svetlichny games. For the two-qubit and three-qubit MNMS, we showed that these states are also the most tolerant state against white noise, and thus serve as valuable quantum resources for such games. In particular, the quantum prediction of the MNMS decreases as the linear entropy increases, and then ceases to be nonlocal when the linear entropy reaches the critical points ${2}/{3}$ and ${9}/{14}$ for the two- and three-qubit cases, respectively. The MNMS are related to classical errors in experimental preparation of maximally entangled states.