Graph States for Quantum Secret Sharing

TL;DR

This paper demonstrates how graph states unify various quantum secret sharing models, generalizes classical secret sharing thresholds, and introduces embedded protocols for quantum information processing.

Contribution

It provides a unified graph state framework for quantum secret sharing, generalizes threshold schemes, and introduces embedded protocols within larger graph states.

Findings

Unified quantum secret sharing models using graph states

Generalized threshold classical secret sharing over insecure channels

Embedded protocols within larger graph states for quantum processing

Abstract

We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by graph states, our approach provides a generalization of threshold classical secret sharing via insecure quantum channels beyond the current requirement of 100% collaboration by players to just a simple majority in the case of five players. Another innovation here is the introduction of embedded protocols within a larger graph state that serves as a one-way quantum information processing system.