Computationally Efficient Nonlinear Bell Inequalities for General Quantum Networks

TL;DR

This paper introduces computationally efficient nonlinear Bell inequalities for general quantum networks, enabling better characterization of multipartite quantum correlations and violations with various quantum states.

Contribution

It presents explicit, polynomial-time constructible Bell inequalities for general networks, including cyclic ones, improving upon previous methods.

Findings

Maximal violations with EPR and GHZ states.

Violations also hold for Werner and noisy states.

Inequalities are suitable for experimental quantum network characterization.

Abstract

The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The main problem is that no computationally efficient method is available for constructing useful Bell inequalities for general quantum networks. In this work, we show a significant improvement by presenting new, explicit Bell-type inequalities for general networks including cyclic networks. These nonlinear inequalities are related to the matching problem of an equivalent unweighted bipartite graph that allows constructing a polynomial-time algorithm. For the quantum resources consisting of bipartite entangled pure states and generalized Greenberger-Horne-Zeilinger (GHZ) states, we prove the generic non-multilocality of quantum networks with multiple independent observers using new Bell inequalities. The violations are maximal with respect to the presented Tsirelson's bound for Einstein-Podolsky-Rosen (EPR) states and GHZ states. Moreover, these violations hold for Werner states or some general noisy states. Our results suggest that the presented Bell inequalities can be used to characterize experimental quantum networks.