Experimentally Feasible Security Check for n-qubit Quantum Secret Sharing

TL;DR

This paper proposes a practical security check for n-qubit quantum secret sharing protocols, especially for multipartite GHZ states, using an inequality to detect genuine n-partite entanglement and ensure security.

Contribution

It introduces a feasible security verification method for generalized n-party quantum secret sharing schemes based on multipartite entanglement detection.

Findings

The multipartite HBB scheme is insecure in some settings.

The proposed inequality effectively detects genuine n-partite entanglement.

The security check is practical for large n-party quantum secret sharing.

Abstract

In this article we present a general security strategy for quantum secret sharing (QSS) protocols based on the HBB scheme presented by Hillery, Bu\v{z}ek and Berthiaume [Phys. Rev A \textbf{59}, 1829 (1999)]. We focus on a generalization of the HBB protocol to $n$ communication parties thus including $n$-partite GHZ states. We show that the multipartite version of the HBB scheme is insecure in certain settings and impractical when going to large $n$. To provide security for such QSS schemes in general we use the framework presented by some of the authors [M. Huber, F. Minert, A. Gabriel, B. C. Hiesmayr, Phys. Rev. Lett. \textbf{104}, 210501 (2010)] to detect certain genuine $n$ partite entanglement between the communication parties. In particular, we present a simple inequality which tests the security.