Witnessing nonlocality in quantum network of continuous-variable systems by generalized quasiprobability functions

TL;DR

This paper introduces nonlinear Bell-type inequalities based on generalized quasiprobability functions to witness nonlocality in continuous-variable quantum networks, enabling experimental verification of network nonlocality.

Contribution

It proposes a novel method utilizing non-Gaussian measurements and generalized quasiprobability functions to detect nonlocality in CV quantum networks with various configurations.

Findings

The inequalities depend solely on generalized quasiprobability functions of Gaussian states.

The approach effectively witnesses nonlocality in chain, star, tree, and cyclic CV networks.

The method provides clear recipes for experimental verification of network nonlocality.

Abstract

Gaussian measurements can not be used to witness nonlocality in Gaussian states as well as the network nonlocality in networks of continuous-variable (CV) systems. Thus special non-Gaussian measurements have to be utilized. In the present paper, we first propose a kind of nonlinear Bell-type inequality that is applicable to quantum networks of both finite or infinite dimensional systems. Violation of the inequality will witness the network nonlocality. This inequality allows us to propose a method of the supremum strategy for detecting network nonlocality in CV systems with source states being any multipartite multi-mode Gaussian states according to the configurations of the networks by utilizing non-Gaussian measurements based on generalized quasiprobability functions. The nonlinear Bell-type inequalities for CV networks, which depend solely on the generalized quasiprobability functions of Gaussian states, are straightforward to construct and implement. As illustrations, we propose the corresponding nonlinear Bell-type inequalities for any chain, star, tree-shaped and cyclic networks in CV systems with source states being $(1+1)$-mode Gaussian states. The examples show that this approach works well for witnessing the nonlocality in networks of CV systems. Particularly, a thorough discussion is given for the entanglement swapping network. Our study provide a strong signature for the network nonlocality nature of CV systems and lead to precise recipes for its experimental verification.