Exploring Bell nonlocality of quantum networks with stabilizing and logical operators

TL;DR

This paper introduces a novel approach to exploring Bell nonlocality in quantum networks by utilizing stabilizer and logical operators, deriving new inequalities, and designing local measurements to demonstrate quantum nonlocality with minimal state knowledge.

Contribution

It presents a new method using stabilizer and logical operators to analyze Bell nonlocality in quantum networks, deriving associated inequalities and measurement strategies.

Findings

Derived nonlinear Bell inequalities for quantum networks.

Designed local incompatible observables for inequality violation.

Explored maximal violation strategies for non-maximal entangled states.

Abstract

In practical quantum networks, a variety of multi-qubit stabilized states emitted from independent sources are distributed among the agents, and the correlations across the entire network can be derived from each agent's local measurements on the shared composite quantum systems. To reveal the Bell non-locality in such cases as a quantum feature, minimal knowledge of the emitted stabilizer state is required. Here, we demonstrate that knowing the stabilizing and logical operators indeed provides a new way of exploring Bell non-locality in quantum networks. For the qubit distribution in quantum networks, the associated nonlinear Bell inequalities are derived. On the other hand, to violate these inequalities, one can design local incompatible observables using minimal knowledge of the emitted states. The tilted nonlinear Bell inequalities tailored for specific non-maximal entangled stabilizer states and a way of achieving the maximal violation are also explored.