We develop a connection between tripartite information I3, secret sharing protocols and multi-unitaries. This leads to explicit ((2,3)) threshold schemes in arbitrary dimension minimizing tripartite information I3. As an application we show that Page scrambling unitaries simultaneously work for all secrets shared by Alice. Using the I3-Ansatz for imperfect sharing schemes we discover examples of VIP sharing schemes.
@article{arxiv.2012.08445,
title = {Quantum Secret Sharing and Tripartite Information},
author = {Marius Junge and Chloe Kim and Guangkuo Liu and Peixue Wu},
journal= {arXiv preprint arXiv:2012.08445},
year = {2020}
}