A unified framework for Bell inequalities from continuous-variable contextuality

TL;DR

This paper introduces a universal framework for analyzing Bell inequalities across continuous, discrete, and hybrid quantum systems, enabling the identification of optimal inequalities and revealing new non-local states.

Contribution

It presents a dimension-agnostic formalism that unifies continuous-variable non-locality studies and discovers novel states exhibiting Bell non-locality.

Findings

First example of continuous-variable non-locality not mappable to CHSH

Framework finds optimal Bell inequalities for any measurement scenario

Identifies hybrid states capable of Bell inequality violation in near term

Abstract

Although the original EPR paradox was formulated in terms of position and momentum, most studies of these phenomena have focused on measurement scenarios with only a discrete number of possible measurement outcomes. Here, we present a framework for studying non-locality that is agnostic to the dimension of the physical systems involved, allowing us to probe purely continuous-variable, discrete-variable, or hybrid non-locality. Our approach allows us to find the optimal Bell inequality for any given measurement scenario and quantifies the amount of non-locality that is present in measurement statistics. This formalism unifies the existing literature on continuous-variable non-locality and allows us to identify new states in which Bell non-locality can be probed through homodyne detection. Notably, we find the first example of continuous-variable non-locality that cannot be mapped to a CHSH Bell inequality. Moreover, we provide several examples of simple hybrid DV-CV entangled states that could lead to near-term violation of Bell inequalities.