With the rapid progress of quantum cryptography, secret sharing has been developed in the quantum setting for achieving a high level of security, which is known as quantum secret sharing (QSS). The first QSS scheme was proposed by Hillery et al. in 1999 [Phys. Rev. A, Vol. 59, p.1829 (1999)] based on entangled Greenberger-Horne-Zeilinger (GHZ) states. However, only 50% of the entangled quantum states are effective for eavesdropping detection and secret splitting in the original scheme. In this paper, we introduce a possible method, called measurement-delay strategy, to improve the qubit efficiency of the GHZ-based QSS scheme. By using this method, the qubit efficiency of the improved QSS scheme can reach 100% for both security detection and secret distribution. The improved QSS scheme can be implemented experimentally based on current technologies.
With the rapid progress of quantum cryptography, secret sharing has been developed in the quantum setting for achieving a high level of security, which is known as quantum secret sharing (QSS). The first QSS scheme was proposed by Hillery et al. in 1999 [Phys. Rev. A, Vol. 59, p.1829 (1999)] based on entangled Greenberger-Horne-Zeilinger (GHZ) states. However, only 50% of the entangled quantum states are effective for eavesdropping detection and secret splitting in the original scheme. In this paper, we introduce a possible method, called measurement-delay strategy, to improve the qubit efficiency of the GHZ-based QSS scheme. By using this method, the qubit efficiency of the improved QSS scheme can reach 100% for both security detection and secret distribution. The improved QSS scheme can be implemented experimentally based on current technologies.
In a recent work, Markham and Sanders proposed a framework to study quantum secret-sharing (QSS) schemes using graph states. This framework unified three classes of QSS protocols, namely, sharing classical secrets over private and public channels, and sharing quantum secrets. However, previous work on graph-state secret sharing mostly focused on threshold schemes. In this paper, we focus on general access structures. We show how to realize a large class of arbitrary access structures using the graph-state formalism. We show an equivalence between
[[n,1]] binary quantum codes and graph-state secret-sharing schemes sharing one bit. We also establish a similar (but restricted) equivalence between a class of
[[n,1]] Calderbank-Shor-Steane codes and graph-state QSS schemes sharing one qubit. With these results we are able to construct a large class of graph-state quantum secret-sharing schemes with arbitrary access structures.