Exploring Bell nonlocality of quantum networks with stabilizing and logical operators

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.

21 pages, 2 figures

References in corpus (8)

• Device-independent security of quantum cryptography against collective attacks
• Multi-party entanglement in graph states
• Bell Inequalities for Graph States
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Classical simulation of entanglement swapping with bounded communication
• Mermin inequalities for perfect correlations
• Generalized Ardehali-Bell inequalities for graph states
• Multipartite unlockable bound entanglement in the stabilizer formalism