{"title":"Quantum secret sharing scheme based on prime dimensional locally distinguishable states","authors":"Kexin Hu, Zhihui Li, Xingjia Wei, Haozhe Duan","doi":"10.1007/s11128-024-04496-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we first study the maximally commutative set in prime dimensional systems, which is a set of generalized Pauli matrices, and it can be used to detect the local discrimination of generalized Bell states. We give a simple characterization of prime dimensional maximally commutative sets, that is, a subset of a set of generalized Bell states, whose second subscript is a multiple of the first subscript. Furthermore, some sets of generalized Bell states which can be locally distinguishable by one-way local operation and classical communication (LOCC) are constructed by using the structural characteristics of prime dimensional maximally commutative sets. Based on these distinguishable generalized Bell states, we propose a (<i>t</i>, <i>n</i>)-threshold quantum secret sharing scheme. Compared with the existing quantum secret sharing scheme, it can be found that there are enough distinguishable states to encode classical information in our scheme, the dealer only needs to send entangled particles once to make the participants get their secret share, which makes the secret sharing process more efficient than the existing schemes. Finally, we prove that this protocol is secure under dishonest participant attack, interception-and-resend attack and entangle-and-measure attack.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11128-024-04496-6","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we first study the maximally commutative set in prime dimensional systems, which is a set of generalized Pauli matrices, and it can be used to detect the local discrimination of generalized Bell states. We give a simple characterization of prime dimensional maximally commutative sets, that is, a subset of a set of generalized Bell states, whose second subscript is a multiple of the first subscript. Furthermore, some sets of generalized Bell states which can be locally distinguishable by one-way local operation and classical communication (LOCC) are constructed by using the structural characteristics of prime dimensional maximally commutative sets. Based on these distinguishable generalized Bell states, we propose a (t, n)-threshold quantum secret sharing scheme. Compared with the existing quantum secret sharing scheme, it can be found that there are enough distinguishable states to encode classical information in our scheme, the dealer only needs to send entangled particles once to make the participants get their secret share, which makes the secret sharing process more efficient than the existing schemes. Finally, we prove that this protocol is secure under dishonest participant attack, interception-and-resend attack and entangle-and-measure attack.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.