Measurement Incompatibility Based In-equivalence Between Bell and Network Nonlocality

This paper demonstrates that the necessity of measurement incompatibility for generating non-local correlations in quantum networks is topology-dependent, revealing that non-linear networks require incompatible measurements from all parties, star networks require at least one, while linear networks with $n>2$ can exhibit non-locality even when all parties perform compatible measurements, and that incompatibility alone is insufficient for non-locality detection in any network.

Original authors: Kaushiki Mukherjee, Biswajit Paul