{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:55:50Z","timestamp":1760151350983,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,8]],"date-time":"2022-03-08T00:00:00Z","timestamp":1646697600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62176273, 61962009, U1936216"],"award-info":[{"award-number":["62176273, 61962009, U1936216"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Open Fund of Advanced Cryptography and System Security Key Laboratory of Sichuan Province","award":["SKLACSS-202101)"],"award-info":[{"award-number":["SKLACSS-202101)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum information splitting (QIS) provides an idea for transmitting the quantum state through a classical channel and a preshared quantum entanglement resource. This paper presents a new scheme for QIS based on a five-qubit cluster state and a Bell state. In this scheme, the sender transmits the unknown three-qubit secret state to two agents by the quantum channel with the Bell basis measurement three times and broadcasts the measurement results to the agents through the classical channel. The agent who restores the secret state can successfully recover the initial information to be transmitted through the appropriate unitary operation with the help of the other party. Firstly, our scheme\u2019s process can be accurately realized by performing the applicable Bell basis measurement, single-qubit measurement, and local unitary operation instead of a multiparticle joint measurement. The splitting process of quantum information is realized through a convenient operation. Secondly, compared with some previous schemes, the efficiency of the total scheme has been improved in principle, and the qubit consumption is reduced. Finally, the security of the quantum information splitting scheme is analyzed from the perspectives of external attacks and participant attacks. It is proved that our scheme can effectively resist internal participant attacks and external eavesdropper attacks.<\/jats:p>","DOI":"10.3390\/e24030381","type":"journal-article","created":{"date-parts":[[2022,3,8]],"date-time":"2022-03-08T12:35:37Z","timestamp":1646742937000},"page":"381","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Splitting an Arbitrary Three-Qubit State via a Five-Qubit Cluster State and a Bell State"],"prefix":"10.3390","volume":"24","author":[{"given":"Gang","family":"Xu","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, North China University of Technology, Beijing 100144, China"},{"name":"Advanced Cryptography and System Security Key Laboratory of Sichuan Province, Chengdu 610025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianai","family":"Zhou","sequence":"additional","affiliation":[{"name":"Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiu-Bo","family":"Chen","sequence":"additional","affiliation":[{"name":"Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4674-7711","authenticated-orcid":false,"given":"Xiaojun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Dublin City University, D09 W6Y4 Dublin, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1109\/TSC.2019.2927215","article-title":"BOEW: A content-based image retrieval scheme using bag-of-encrypted-words in cloud computing","volume":"15","author":"Xia","year":"2019","journal-title":"IEEE Trans. Serv. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1109\/TPDS.2015.2401003","article-title":"A Secure and Dynamic Multi-keyword Ranked Search Scheme over Encrypted Cloud Data","volume":"27","author":"Xia","year":"2015","journal-title":"IEEE Trans. Parallel. Distrib. Syst."},{"key":"ref_3","first-page":"809","article-title":"Controlled secure direct communication protocol via the three-qubit partially entangled set of states","volume":"58","author":"Xu","year":"2019","journal-title":"Comput. Mater. Contin."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"89","DOI":"10.32604\/jqc.2019.07415","article-title":"Anti-Noise Quantum Network Coding Protocol Based on Bell States and Butterfly Network Model","volume":"1","author":"Zhang","year":"2019","journal-title":"J. Quantum Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"273","DOI":"10.32604\/iasc.2021.018120","article-title":"Measurement-based quantum repeater network coding","volume":"30","author":"Chen","year":"2021","journal-title":"Intell. Autom. Soft Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1126\/science.1253512","article-title":"Unconditional quantum teleportation between distant solid-state quantum bits","volume":"345","author":"Pfaff","year":"2014","journal-title":"Science"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4394","DOI":"10.1103\/PhysRevA.58.4394","article-title":"Quantum teleportation using three-particle entanglement","volume":"58","author":"Karlsson","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"022338","DOI":"10.1103\/PhysRevA.72.022338","article-title":"Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement","volume":"72","author":"Deng","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2331","DOI":"10.1016\/j.optcom.2007.12.002","article-title":"Quantum circuits for controlled teleportation of two-particle entanglement via a W state","volume":"281","author":"Chen","year":"2008","journal-title":"Opt. Commun."},{"key":"ref_10","first-page":"65","article-title":"Controlled quantum teleportation with Bell states","volume":"20","author":"Wang","year":"2011","journal-title":"Chin. Phys. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/S0375-9601(03)00074-4","article-title":"Quantum secret sharing without entanglement","volume":"310","author":"Guo","year":"2003","journal-title":"Phys. Lett. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6130","DOI":"10.1016\/j.optcom.2008.09.026","article-title":"An efficient and secure multiparty quantum secret sharing scheme based on single photons","volume":"281","author":"Wang","year":"2008","journal-title":"Opt. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3647","DOI":"10.1016\/j.optcom.2009.05.054","article-title":"Multiparty quantum secret sharing based on Bell measurement","volume":"282","author":"Sun","year":"2009","journal-title":"Opt. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1007\/s11128-010-0220-z","article-title":"Quantum state sharing of an arbitrary four-qubit GHZ-type state by using a four-qubit cluster state","volume":"10","author":"Nie","year":"2011","journal-title":"QuantumInf. Processing"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1007\/s10773-014-2348-6","article-title":"Splitting an Arbitrary Two-ubit State Via a Seven-qubit Maximally Entangled State","volume":"54","author":"Chen","year":"2015","journal-title":"Int. J. Theor. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.physleta.2005.04.007","article-title":"An efficient quantum secret sharing scheme with Einstein\u2013Podolsky\u2013Rosen pairs","volume":"340","author":"Deng","year":"2005","journal-title":"Phys. Lett. A"},{"key":"ref_17","first-page":"339","article-title":"Probabilistic and hierarchical quantum information splitting based on the non-maximally entangled cluster state","volume":"69","author":"Xu","year":"2021","journal-title":"Comput. Mater. Contin."},{"key":"ref_18","first-page":"171","article-title":"Quantum teleportation and information splitting via four-qubit cluster state and a Bell state","volume":"12","author":"Falaye","year":"2017","journal-title":"Front. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1844","DOI":"10.1007\/s10773-020-04451-y","article-title":"Two-Qubit Quantum State Sharing Protocol Based on Bell State","volume":"59","author":"Ma","year":"2020","journal-title":"Int. J. Theor. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1103\/PhysRevLett.70.1895","article-title":"Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels","volume":"70","author":"Bennett","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1103\/PhysRevA.59.1829","article-title":"Quantum secret sharing","volume":"59","author":"Hillery","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1007\/s11128-014-0800-4","article-title":"Multi-party quantum state sharing of an arbitrary multi-qubit state via \u03c7-type entangled states","volume":"13","author":"Kang","year":"2014","journal-title":"Quantum Inf. Processing"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"044301","DOI":"10.1103\/PhysRevA.72.044301","article-title":"Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein-Podolsky-Rosen pairs","volume":"72","author":"Deng","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s11128-013-0670-1","article-title":"Hierarchical quantum information splitting of an arbitrary two-qubit state via the cluster state","volume":"13","author":"Xu","year":"2014","journal-title":"Quantum Inf. Processing"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1038\/nature02643","article-title":"Experimental demonstration of five-photon entanglement and open-destination teleportation","volume":"430","author":"Zhao","year":"2004","journal-title":"Nature"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5480","DOI":"10.1038\/ncomms6480","article-title":"Experimental demonstration of graph-state quantum secret sharing","volume":"5","author":"Bell","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"062333","DOI":"10.1103\/PhysRevA.78.062333","article-title":"Quantum-information splitting using multipartite cluster states","volume":"78","author":"Muralidharan","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/s11128-012-0379-6","article-title":"Multi-party quantum secret sharing with the single-particle quantum state to encode the information","volume":"12","author":"Chen","year":"2013","journal-title":"Quantum Inf. Processing"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s11128-010-0191-0","article-title":"Multi-party quantum state sharing of an arbitrary two-qubit state with Bell states","volume":"10","author":"Shi","year":"2011","journal-title":"QuantumInf. Processing"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3229","DOI":"10.1007\/s10773-015-2562-x","article-title":"Quantum information splitting of a two-qubit bell state using a five-qubit entangled state","volume":"54","author":"Wang","year":"2015","journal-title":"Int. J. Theor. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s10773-019-04310-5","article-title":"Quantum Information Splitting of Arbitrary Two-Qubit State Via a Five-Qubit Cluster State and a Bell-State","volume":"59","author":"Yang","year":"2020","journal-title":"Int. J. Theor. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s11128-011-0264-8","article-title":"Quantum information splitting of an arbitrary three-qubit state by using a genuinely entangled five-qubit state and a Bell-state","volume":"11","author":"Nie","year":"2012","journal-title":"Quantum Inf. Processing"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4616","DOI":"10.1016\/j.optcom.2012.06.044","article-title":"Quantum information splitting of an arbitrary three-qubit state via the cavity input\u2013output process","volume":"285","author":"Zhong","year":"2012","journal-title":"Opt. Commun."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"062303","DOI":"10.1103\/PhysRevA.68.062303","article-title":"Quantum computation based on d-Level cluster state","volume":"68","author":"Zhou","year":"2003","journal-title":"Phys. Rev. A"},{"key":"ref_35","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."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5250","DOI":"10.1007\/s10773-016-3146-0","article-title":"Quantum Information Splitting of Arbitrary Three-qubit State by Using Five-qubit Cluster state and GHZ-state","volume":"55","author":"Yin","year":"2016","journal-title":"Int. J. Theor. 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