Characterizing nonlocal correlations through various $n$-locality inequlities in quantum network

TL;DR

This paper introduces new $n$-locality inequalities for quantum networks with multiple parties, demonstrating their violations and correspondence with Bell inequalities without assuming system dimensions, thus advancing understanding of quantum nonlocality.

Contribution

The work generalizes network nonlocality to star-network topologies with arbitrary measurements, proposing new inequalities and establishing their relation to Bell inequalities without system dimension assumptions.

Findings

Demonstrated violations of $n$-locality inequalities in star networks.

Established correspondence between $n$-locality violations and chained Bell inequalities.

Extended analysis to cases requiring multiple copies of entangled states.

Abstract

The multipartite quantum networks feature multiple independent sources, in contrast to the conventional multipartite Bell experiment involving a single source. So far, network nonlocality has been explored when each source produces a two-qubit entangled state. In this work, we demonstrate the network nonlocality when each party performs a black-box measurement, and the dimension of the system remains unspecified. In an interesting work, by considering each source produces two-qubit entangled states in the conventional bilocal scenario, Gisin \emph{et. al.} in https://doi.org/10.1103/PhysRevA.96.020304] demonstrated a correspondence between the violations of bipartite Clauser-Horne-Shimony-Halt inequality and the bilocality inequality. We introduce a variant of the sum-of-squares approach to reproduce their results without assuming the dimension of the system. We then generalize the argument for network nonlocality in star-network topology. Further, we propose a new set of $n$-locality inequalities in star-network configuration where each of the $n$ parties performs an arbitrary number of dichotomic measurements and demonstrate the above correspondence between the quantum violations of the $n$-locality inequalities and the chained Bell inequalities. A similar correspondence is demonstrated based on a recently formulated family of $n$-locality inequalities whose optimal quantum violation cannot be obtained when each source emits a two-qubit entangled state and requires multiple copies of two-qubit entangled states. Throughout this paper, each party in the network performs black-box measurements, and the dimension of the system remains unspecified.