{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T16:22:58Z","timestamp":1778343778310,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,30]],"date-time":"2023-04-30T00:00:00Z","timestamp":1682812800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61872284"],"award-info":[{"award-number":["61872284"]}]},{"name":"National Natural Science Foundation of China","award":["61671087"],"award-info":[{"award-number":["61671087"]}]},{"name":"National Natural Science Foundation of China","award":["61962009"],"award-info":[{"award-number":["61962009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Semi-quantum cryptography communication stipulates that the quantum user has complete quantum capabilities, and the classical user has limited quantum capabilities, only being able to perform the following operations: (1) measuring and preparing qubits with a Z basis and (2) returning qubits without any processing. Secret sharing requires participants to work together to obtain complete secret information, which ensures the security of the secret information. In the semi-quantum secret sharing (SQSS) protocol, the quantum user Alice divides the secret information into two parts and gives them to two classical participants. Only when they cooperate can they obtain Alice\u2019s original secret information. The quantum states with multiple degrees of freedom (DoFs) are defined as hyper-entangled states. Based on the hyper-entangled single-photon states, an efficient SQSS protocol is proposed. The security analysis proves that the protocol can effectively resist well-known attacks. Compared with the existing protocols, this protocol uses hyper-entangled states to expand the channel capacity. The transmission efficiency is 100% higher than that of single-degree-of-freedom (DoF) single-photon states, providing an innovative scheme for the design of the SQSS protocol in quantum communication networks. This research also provides a theoretical basis for the practical application of semi-quantum cryptography communication.<\/jats:p>","DOI":"10.3390\/e25050742","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T12:14:08Z","timestamp":1682943248000},"page":"742","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A Semi-Quantum Secret-Sharing Protocol with a High Channel Capacity"],"prefix":"10.3390","volume":"25","author":[{"given":"Yuan","family":"Tian","sequence":"first","affiliation":[{"name":"College of Information and Control Engineering, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Genqing","family":"Bian","sequence":"additional","affiliation":[{"name":"College of Information and Control Engineering, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinyong","family":"Chang","sequence":"additional","affiliation":[{"name":"College of Information and Control Engineering, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Information and Control Engineering, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Li","sequence":"additional","affiliation":[{"name":"School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chongqiang","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1145\/359168.359176","article-title":"How to share a secret","volume":"22","author":"Shamir","year":"1979","journal-title":"Commun. ACM"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3512344","article-title":"A Survey on Perfectly Secure Verifiable Secret-Sharing","volume":"54","author":"Chandramouli","year":"2022","journal-title":"ACM Comput. Surv. CSUR"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Blanton, M., Kang, A., and Yuan, C. (2020, January 19\u201322). Improved building blocks for secure multi-party computation based on secret sharing with honest majority. Proceedings of the Applied Cryptography and Network Securit: 18th International Conference, ACNS 2020, Rome, Italy.","DOI":"10.1007\/978-3-030-57808-4_19"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1007\/s11280-018-0575-0","article-title":"E-voting scheme using secret sharing and K-anonymity","volume":"22","author":"Liu","year":"2019","journal-title":"World Wide Web"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1103\/RevModPhys.74.145","article-title":"Quantum cryptography","volume":"74","author":"Gisin","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"025008","DOI":"10.1103\/RevModPhys.94.025008","article-title":"Security in quantum cryptography","volume":"94","author":"Portmann","year":"2022","journal-title":"Rev. Mod. Phys."},{"key":"ref_7","unstructured":"Bennett, C.H., and Brassard, G. (1984, January 10\u201312). Quantum cryptography: Public key distribution and coin tossing. Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1038\/nphoton.2014.149","article-title":"Secure quantum key distribution","volume":"8","author":"Lo","year":"2016","journal-title":"Nat. Photonics"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5778","DOI":"10.1109\/TCOMM.2020.3006201","article-title":"Toward practical quantum secure direct communication: A quantum-memory-free protocol and code design","volume":"68","author":"Sun","year":"2020","journal-title":"IEEE Trans. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"eabe6379","DOI":"10.1126\/sciadv.abe6379","article-title":"Quantum key distribution with entangled photons generated on demand by a quantum dot","volume":"7","author":"Valeri","year":"2021","journal-title":"Sci. Adv."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1103\/PhysRevA.59.1829","article-title":"Berthiaume, Quantum secret sharing","volume":"59","author":"Hillery","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"062311","DOI":"10.1103\/PhysRevA.99.062311","article-title":"Quantum secret sharing with polarization-entangled photon pairs","volume":"99","author":"Williams","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s11128-019-2571-4","article-title":"Efficient quantum secret sharing without a trusted player","volume":"19","author":"Sutradhar","year":"2020","journal-title":"Quantum Inf. Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"032410","DOI":"10.1103\/PhysRevA.103.032410","article-title":"Quantum secret sharing using discretely modulated coherent states","volume":"103","author":"Liao","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2881","DOI":"10.1103\/PhysRevLett.69.2881","article-title":"Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states","volume":"69","author":"Bennett","year":"1992","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1515\/nanoph-2020-0351","article-title":"Quantum computing and simulation: Where we stand and what awaits US","volume":"10","author":"Cirac","year":"2020","journal-title":"Nanophotonics"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Boyer, M., Kenigsberg, D., and Mor, T. (2007, January 2\u20136). Quantum key distribution with classical Bob. Proceedings of the 2007 First International Conference on Quantum, Nano, and Micro Technologies (ICQNM\u201907), Guadeloupe, France.","DOI":"10.1109\/ICQNM.2007.18"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s11128-020-2595-9","article-title":"Semi-quantum cryptography","volume":"19","author":"Iqbal","year":"2020","journal-title":"Quantum Inf. Process."},{"key":"ref_19","first-page":"563","article-title":"An efficient semi-quantum key distribution protocol based on EPR and single-particle hybridization","volume":"21","author":"Tian","year":"2021","journal-title":"Quantum Inf. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"966","DOI":"10.3389\/fphy.2022.1023443","article-title":"Multi-party semi-quantum key distribution protocol based on hyperentangled Bell states","volume":"10","author":"Tian","year":"2022","journal-title":"Front. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"035019","DOI":"10.1088\/2058-9565\/ac7412","article-title":"Mediated semi-quantum key distribution with improved efficiency","volume":"7","author":"Guskind","year":"2022","journal-title":"Quantum Sci. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1007\/s11128-020-02674-w","article-title":"Semi-quantum private comparison based on Bell states","volume":"19","author":"Jiang","year":"2020","journal-title":"Quantum Inf. Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s11128-019-2251-4","article-title":"Efficient semi-quantum private comparison using single photons","volume":"18","author":"Lin","year":"2019","journal-title":"Quantum Inf. Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1007\/s11128-021-03294-8","article-title":"An efficient semi-quantum private comparison without pre-shared keys","volume":"20","author":"Tian","year":"2021","journal-title":"Quantum Inf. Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s11128-019-2308-4","article-title":"Semi-quantum identification","volume":"18","author":"Zhou","year":"2019","journal-title":"Quantum Inf. Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1007\/s11128-020-02965-2","article-title":"Mediated semi-quantum secure direct communication","volume":"20","author":"Rong","year":"2021","journal-title":"Quantum Inf. Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"022303","DOI":"10.1103\/PhysRevA.82.022303","article-title":"Semi-quantum secret sharing using entangled states","volume":"82","author":"Li","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"045304","DOI":"10.1088\/1751-8113\/46\/4\/045304","article-title":"Quantum secret sharing with classical Bobs","volume":"46","author":"Li","year":"2013","journal-title":"J. Phys. Math. Theor."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3819","DOI":"10.1007\/s10773-015-2622-2","article-title":"A novel semi-quantum secret sharing scheme of specific bits","volume":"54","author":"Xie","year":"2015","journal-title":"Int. J. Theor. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1750150","DOI":"10.1142\/S0217984917501500","article-title":"A novel semi-quantum secret sharing scheme based on Bell states","volume":"31","author":"Yin","year":"2017","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s11128-018-2058-8","article-title":"Limited resource semiquantum secret sharing","volume":"17","author":"Li","year":"2018","journal-title":"Quantum Inf. Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2883","DOI":"10.1007\/s10773-019-04171-y","article-title":"Limited resource semi-quantum secret sharing based on multi-level systems","volume":"58","author":"Xiang","year":"2019","journal-title":"Int. J. Theor. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1950213","DOI":"10.1142\/S0217732319502134","article-title":"Semi-quantum secret sharing protocol using W-state","volume":"34","author":"Tsai","year":"2019","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s11128-021-03157-2","article-title":"An efficient semi-quantum secret sharing protocol of specific bits","volume":"20","author":"Tian","year":"2021","journal-title":"Quantum Inf. Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1016\/j.cjph.2022.03.031","article-title":"Semi-quantum secret sharing in high-dimensional quantum system using product states","volume":"77","author":"Hu","year":"2022","journal-title":"Chin. J. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1038\/nature14246","article-title":"Quantum teleportation of multiple degrees of freedom of a single photon","volume":"518","author":"Wang","year":"2015","journal-title":"Nature"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2807","DOI":"10.1007\/s10773-020-04540-y","article-title":"Semi-quantum key distribution with single photons in both polarization and spatial-mode degrees of freedom","volume":"59","author":"Ye","year":"2020","journal-title":"Int. J. Theor. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5635","DOI":"10.1103\/PhysRevLett.85.5635","article-title":"Quantum key distribution in the Holevo limit","volume":"85","author":"Cabello","year":"2000","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/742\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:27:31Z","timestamp":1760124451000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/5\/742"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,30]]},"references-count":38,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["e25050742"],"URL":"https:\/\/doi.org\/10.3390\/e25050742","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,30]]}}}