Measurement Incompatibility Based In-equivalence Between Bell and Network Nonlocality

TL;DR

This paper explores how measurement incompatibility influences nonlocal correlations in quantum networks, revealing that non n-locality can occur with compatible measurements in certain topologies, challenging traditional views.

Contribution

It demonstrates that non n-locality can be detected with compatible measurements in linear networks and highlights the topology-dependent role of measurement incompatibility.

Findings

Non n-locality can be detected with a single incompatible measurement in some networks.

Compatible measurements can generate non n-local correlations in linear networks for n>2.

All parties must perform incompatible measurements to generate genuine non n-locality in non-standard networks.

Abstract

It is a well-known fact that measurement incompatibility is a necessary resource to generate nonlocal correlations in usual Bell scenario that typically involves single quantum source. We can provide with some contrasting findings if we consider connected structure of multiple quantum sources. Precisely, we demonstrate that non n-locality can be detected in standard quantum network even when only a single party performs incompatible measurements. More interestingly, for any finite n greater than 2, non n-local correlations can be generated in any standard linear n-local network when all the parties perform compatible measurements. Such an observation is topology specific as one of the parties must perform incompatible measurement to exhibit non n-locality in any non-linear network endowed with star topology. However, we observe that in any non-standard network(all sources independent and nonlocal), to generate genuine non n-local correlations, all the parties must perform incompatible measurements. Such a finding is intuitive as more resource is required to generate stronger form of quantum non-classicality. We also demonstrate that merely providing resource of measurement incompatibility to all the parties is not sufficient for non n-locality detection in any quantum network