Non-Local Boxes for Networks

TL;DR

This paper introduces network nonlocal boxes for quantum networks that adhere to no-signaling and independence principles, characterizing their unique properties in bipartite scenarios with maximal correlations.

Contribution

It defines and analyzes network nonlocal boxes under NSI principles, establishing the uniqueness of certain local and maximal correlation configurations.

Findings

Characterization of network nonlocal boxes satisfying NSI principles.

Proof of uniqueness for local random outputs with maximal 2-box correlations.

Identification of specific correlation values $E_2=rac{ ext{sqrt}(2)-1}$ and $E_2^o=1$.

Abstract

Nonlocal boxes are conceptual tools that capture the essence of the phenomenon of quantum non-locality, central to modern quantum theory and quantum technologies. We introduce network nonlocal boxes tailored for quantum networks under the natural assumption that these networks connect independent sources and do not allow signaling. Hence, these boxes satisfy the No-Signaling and Independence (NSI) principle. For the case of boxes without inputs, connecting pairs of bipartite sources and producing binary outputs, we prove that the sources and boxes producing local random outputs and maximal 2-box correlations, i.e. $E_2=\sqrt{2}-1$, $E_2^o=1$, are essentially unique.