Genuine Bell locality and nonlocality in the networks

TL;DR

This paper investigates genuine Bell nonlocality in quantum networks, proposing new Bell inequalities and demonstrating their maximal quantum violations, highlighting the role of entanglement swapping and the limitations imposed by the no-clone theorem.

Contribution

It introduces novel Bell-type inequalities for quantum networks and analyzes their maximal violations, emphasizing the differences between classical cloning and quantum no-cloning constraints.

Findings

Maximal violations of Bell inequalities are achieved in quantum networks.

Entanglement swapping can replace joint measurements in Bell tests.

Quantum correlations are limited by the no-clone theorem.

Abstract

In the literature on $K$-locality ($K\geq2$) networks, the local hidden variables are strictly distributed in the specific observers rather than the whole ones. Regarding genuine Bell locality, all local hidden variables, as classical objects that allow for perfect cloning in classical physics, should be cloned and then spread throughout the networks. More correlators are involved in the proposed linear and non-linear Bell-type inequalities, where their upper bounds are specified by the pre-determined output probability distribution. As for the quantum version, the no-clone theorem limits the broadcast of quantum correlations. To explore genuine Bell nonlocality in variant particle distributions in the networks, the Pauli operators stabilizing the two-qubit Bell states or multi-qubit Greenberger--Horne--Zeilinger states (GHZ states) play an essential role in designing the proposed linear and non-linear Bell tests and assigning the local incompatible measurements for the spatially separated observers. We prove the maximal violations of the proposed Bell-type inequalities quantum networks. In the end, how entanglement swapping replaces the joint measurements in the Bell tests is demonstrated.