Robust Bell Nonlocality from Gottesman-Kitaev-Preskill States

TL;DR

This paper demonstrates that GKP-encoded states can enable Bell nonlocality tests using homodyne detection in continuous-variable systems, overcoming previous limitations and showing multipartite nonlocality with practical thresholds.

Contribution

It introduces a framework for Bell tests with GKP states using homodyne detection, revealing multipartite nonlocality and quantifying squeezing thresholds and robustness.

Findings

Finitely squeezed GKP-encoded GHZ and W states violate multipartite Bell inequalities.

CHSH inequality cannot be violated for Bell-pair states with this method.

Provides squeezing thresholds and robustness analysis for practical implementation.

Abstract

Bell tests based on homodyne detection are strongly constrained in continuous-variable systems. Can Gottesman-Kitaev-Preskill (GKP) encoding turn homodyne detection into a practical tool for revealing Bell nonlocality? We consider a physically motivated model in which each party performs homodyne detection and digitizes the continuous outcome via a fixed periodic binning, corresponding to logical Pauli measurements. Within this framework, we derive a bipartite no-go: CHSH cannot be violated for Bell-pair states. Moving beyond two parties, we show that finitely squeezed GKP-encoded GHZ and W states nevertheless exhibit strong multipartite nonlocality, violating multipartite Bell inequalities with homodyne-only readout. We quantify the required squeezing thresholds and robustness to loss, providing a route toward homodyne-based Bell tests in continuous-variable systems.