Fine-grained uncertainty relation and biased non-local games in bipartite and tripartite systems

TL;DR

This paper explores how fine-grained uncertainty relations can differentiate classical, quantum, and super-quantum correlations in biased non-local games involving bipartite and tripartite systems, revealing limitations under certain biases.

Contribution

It extends the application of fine-grained uncertainty relations to biased measurement settings in non-local games, highlighting their discriminatory power and limitations.

Findings

Discrimination among correlation types is possible for certain bias ranges.

The ability to distinguish correlations diminishes outside specific bias parameters.

Analytical results show limitations of uncertainty relations under bias.

Abstract

The fine-grained uncertainty relation can be used to discriminate among classical, quantum and super-quantum correlations based on their strength of nonlocality, as has been shown for bipartite and tripartite systems with unbiased measurement settings. Here we consider the situation when two and three parties, respectively, choose settings with bias for playing certain non-local games. We show analytically that while the fine-grained uncertainty principle is still able to distinguish classical, quantum and super-quantum correlations for biased settings corresponding to certain ranges of the biasing parameters, the above-mentioned discrimination is not manifested for all biasing.