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.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.

arXiv:1202.3433Physical Review AOct 1, 201249 citations

Quantum Secret Sharing with Graph States

Sylvain Gravier, Jérôme Javelle, Mehdi Mhalla +1 more

Lecture notes in computer scienceJan 1, 201311 citations

Classical versus Quantum Graph-based Secret Sharing

Jérôme Javelle, Mehdi Mhalla, Simon Perdrix

We study a simple graph-based classical secret sharing scheme: every player's share consists of a random key together with the encryption of the secret with the keys of his neighbours. A characterisation of the authorised and forbidden sets of players is given. Moreover, we show that this protocol is equivalent to the graph state quantum secret sharing (GS-QSS) schemes when the secret is classical. When the secret is an arbitrary quantum state, a set of players is authorised for a GS-QSS scheme if and only if, for the corresponding simple classical graph-based protocol, the set is authorised and its complement set is not.We study a simple graph-based classical secret sharing scheme: every player's share consists of a random key together with the encryption of the secret with the keys of his neighbours. A characterisation of the authorised and forbidden sets of players is given. Moreover, we show that this protocol is equivalent to the graph state quantum secret sharing (GS-QSS) schemes when the secret is classical. When the secret is an arbitrary quantum state, a set of players is authorised for a GS-QSS scheme if and only if, for the corresponding simple classical graph-based protocol, the set is authorised and its complement set is not.

arXiv:1109.4731Sep 22, 20115 citations

Experimental demonstration of graph-state quantum secret sharing

Bryn A. Bell, Damian Markham, David A. Herrera-Martí +4 more

arXiv:1411.5827Nature CommunicationsNov 21, 2014165 citations

Free-Space Continuous-Variable Quantum Secret Sharing

Fangli Yang, Liang Chang, Daowen Qiu +1 more

Free-space quantum cryptography holds significant potential for enabling global quantum communication networks. This paper proposes a free-space continuous-variable quantum secret sharing (CV-QSS) protocol employing a local local oscillator (LLO). The proposed protocol simplifies the system architecture by requiring only two heterodyne detections at the dealer’s side, thereby eliminating the additional noise and complexity associated with coherent measurements at each participant’s side in conventional schemes. Theoretically, we establish a channel transmittance model that comprehensively incorporates the effects of rain extinction and atmospheric turbulence, and derive the bound of the secret key rate. Experimentally, we systematically evaluate the impact of weather conditions and atmospheric turbulence on protocol performance and conduct comparative evaluations against existing schemes. The results demonstrate that the proposed protocol outperforms the previously proposed free-space LLO-based CV-QSS protocol in terms of key rate, transmission distance, noise tolerance, and participant capacity. Furthermore, this protocol supports secret sharing among 5 participants over 75 km or up to 37 participants within 10 km, outperforming the LLO-based CV-QSS system in a fiber channel. This study validates the potential of free-space CV-QSS as a viable solution for medium-to-long-distance and multi-user quantum secret sharing.Free-space quantum cryptography holds significant potential for enabling global quantum communication networks. This paper proposes a free-space continuous-variable quantum secret sharing (CV-QSS) protocol employing a local local oscillator (LLO). The proposed protocol simplifies the system architecture by requiring only two heterodyne detections at the dealer’s side, thereby eliminating the additional noise and complexity associated with coherent measurements at each participant’s side in conventional schemes. Theoretically, we establish a channel transmittance model that comprehensively incorporates the effects of rain extinction and atmospheric turbulence, and derive the bound of the secret key rate. Experimentally, we systematically evaluate the impact of weather conditions and atmospheric turbulence on protocol performance and conduct comparative evaluations against existing schemes. The results demonstrate that the proposed protocol outperforms the previously proposed free-space LLO-based CV-QSS protocol in terms of key rate, transmission distance, noise tolerance, and participant capacity. Furthermore, this protocol supports secret sharing among 5 participants over 75 km or up to 37 participants within 10 km, outperforming the LLO-based CV-QSS system in a fiber channel. This study validates the potential of free-space CV-QSS as a viable solution for medium-to-long-distance and multi-user quantum secret sharing.

arXiv:2503.11263IEEE Transactions on Green Communications and NetworkingDec 11, 20251 citation

Quantum secret sharing with continuous variable graph state

Yadong Wu, Runze Cai, Guangqiang He +1 more

arXiv:1304.4477Quantum Information ProcessingDec 16, 201316 citations

[[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.