# Local marginals ameliorate device independent witnessing of genuine entanglement

## TL;DR

This paper demonstrates that local marginal distributions can serve as semi-device independent witnesses for genuine multipartite entanglement, even at the critical violation threshold of Mermin's inequality, with potential for full device independence.

## Contribution

It shows that local marginals can certify genuine entanglement at the MI threshold, extending device independence in multipartite entanglement detection.

## Key findings

- Local marginals suffice as semi-device independent witnesses.
- Genuine entanglement can be certified at the MI threshold with local marginals.
- Full device independence is achievable using Mermin polynomial-based quantities.

## Abstract

We consider the problem of determining the presence of genuine multipartite entanglement through the violation of Mermin's Bell-type inequality (MI). Though the violation of MI cannot certify the presence of genuine nonlocality, but can certify genuine tripartite entanglement whenever the violation is strictly greater than $2\sqrt{2}$. Here we show that MI suffices as genuine entanglement witness even when its value is $2\sqrt{2}$ if at least two of the local marginal distributions are not completely random provided the local Hilbert space dimension of at least one of the sub-systems is two. Thus local marginals suffice as semi-device independent genuine entanglement witness. This is intriguing in a sense, as the local properties of a composite system can help to identify its global property. Furthermore, analyzing another quantity constructed from Mermin polynomials we show that genuine entanglement certification task for the correlations with MI violation equal to $2\sqrt{2}$ can actually be made fully device independent.