Graph States for Quantum Secret Sharing

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.

This version amends the original security claim for QQ (n,n): in fact the secret is not completely denied to the adversary in this case. We thank S. Perdrix, B. Fortescue and G. Gour for pointing out the error. The changes are detailed in D. Markham and B. C. Sanders, "Erratum: Graph states for quantum secret sharing [Phys. Rev. A 78, 042309 (2008)]", Phys. Rev. A 83, 019901(E) (2011)

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