Observers can always generate nonlocal correlations without aligning measurements by covering all their bases

TL;DR

This paper proves that two parties sharing a Bell state and choosing three random orthogonal measurements always violate a Bell inequality, regardless of measurement alignment, and this violation is robust against noise, with implications for multi-party scenarios.

Contribution

It demonstrates that random measurement bases suffice for Bell inequality violation without alignment, enhancing robustness against noise and extending to multiple parties.

Findings

Always violate Bell inequality with random orthogonal measurements

Robust against local depolarizing noise

Increased robustness with more parties

Abstract

Quantum theory allows for correlations between the outcomes of distant measurements that are inconsistent with any locally causal theory, as demonstrated by the violation of a Bell inequality. Typical demonstrations of these correlations require careful alignment between the measurements, which requires distant parties to share a reference frame. Here, we prove, following a numerical observation by Shadbolt et al., that if two parties share a Bell state and each party randomly chooses three orthogonal measurements, then the parties will always violate a Bell inequality. Furthermore, we prove that this probability is highly robust against local depolarizing noise, in that small levels of noise only decrease the probability of violating a Bell inequality by a small amount. We also show that generalizing to N parties increases the robustness against noise. These results improve on previous ones that only allowed a high probability of violating a Bell inequality for large numbers of parties.