Quantum Secret Sharing and Tripartite Information

TL;DR

This paper explores the relationship between tripartite information, secret sharing protocols, and multi-unitaries, introducing explicit threshold schemes and analyzing their properties, including applications to Page scrambling unitaries and VIP sharing schemes.

Contribution

It establishes a novel connection between tripartite information and secret sharing, providing explicit threshold schemes and analyzing their effectiveness in quantum information sharing.

Findings

Explicit ((2,3)) threshold schemes minimizing tripartite information in arbitrary dimensions.

Page scrambling unitaries work for all secrets shared by Alice.

Discovery of VIP sharing schemes using the $I_3$-Ansatz for imperfect sharing.

Abstract

We develop a connection between tripartite information $I_3$, secret sharing protocols and multi-unitaries. This leads to explicit ((2,3)) threshold schemes in arbitrary dimension minimizing tripartite information $I_3$. As an application we show that Page scrambling unitaries simultaneously work for all secrets shared by Alice. Using the $I_3$-Ansatz for imperfect sharing schemes we discover examples of VIP sharing schemes.