Correlations In n-local Scenario

TL;DR

This paper extends Bell-type inequalities to n+1 party scenarios, deriving tight bounds and demonstrating quantum violations, but finds that increasing parties does not improve noise resistance compared to bilocal scenarios.

Contribution

It introduces n-local Bell inequalities for multi-party scenarios, proving their tightness and analyzing quantum violations in these extended networks.

Findings

Derived tight n-local inequalities for multi-party scenarios.

Quantum violations observed with maximally entangled states.

Noise resistance does not improve with more parties compared to bilocal case.

Abstract

Recently Bell-type inequalities were introduced in Phys. Rev. A \textbf{85}, 032119 (2012) to analyze the correlations emerging in an entanglement swapping scenario characterized by independence of the two sources shared between three parties. The corresponding scenario was referred to as \textit{bilocal} scenario. Here, we derive Bell-type inequalities in $n+1$ party scenario, i.e., in $n$-local scenario. Considering the two different cases with several number of inputs and outputs, we derive local and $n$-local bounds. The $n$-local inequality studied for two cases are proved to be tight. Replacing the sources by maximally entangled states for two binary inputs and two binary outputs and also for the fixed input and four outputs, we observe quantum violations of $n$-local bounds. But the resistance offered to noise cannot be increased as compared to the bilocal scenario. Thus increasing the number of parties in a linear fashion in source independent scenario does not contribute in lowering down the requirements of revealing quantumness in a network in contrast to the star configuration (Phys. Rev. A \textbf{90}, 062109 (2014)) of $n+1$ parties.