Improvement in device-independent witnessing of genuine tripartite entanglement by local marginals
Physical Review A
We consider the problem of determining the presence of genuine tripartite entanglement through the violation of Mermin inequality. Although the violation of Mermin inequality cannot certify the presence of genuine nonlocality, it can certify the presence of genuine tripartite entanglement whenever the violation is strictly greater than 22. Here we show that Mermin inequality suffices as a genuine entanglement witness even when its value is 22 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 subsystems is 2. Thus local marginals suffice as a 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 the genuine entanglement certification task for the correlations with Mermin inequality violation equal to 22 can actually be made fully device independent.
Bhattacharya, Some Sankar; Paul, Biswajit; Roy, Arup; Mukherjee, Amit; Jebaratnam, C.; and Banik, Manik, "Improvement in device-independent witnessing of genuine tripartite entanglement by local marginals" (2017). Journal Articles. 2601.