{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:04:42Z","timestamp":1760234682120,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T00:00:00Z","timestamp":1622764800000},"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":["61801420"],"award-info":[{"award-number":["61801420"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key-Area Research and Development Program of Guangdong Province","award":["2020B0303040001"],"award-info":[{"award-number":["2020B0303040001"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["020414380141"],"award-info":[{"award-number":["020414380141"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As an essential application of quantum mechanics in classical cryptography, quantum secret sharing has become an indispensable component of quantum internet. Recently, a differential phase shift quantum secret sharing protocol using a twin field has been proposed to break the linear rate-distance boundary. However, this original protocol has a poor performance over channels with asymmetric transmittances. To make it more practical, we present a differential phase shift quantum secret sharing protocol with asymmetric source intensities and give the security proof of our protocol against individual attacks. Taking finite-key effects into account, our asymmetric protocol can theoretically obtain the key rate two orders of magnitude higher than that of the original protocol when the difference in length between Alice\u2019s channel and Bob\u2019s is fixed at 14 km. Moreover, our protocol can provide a high key rate even when the difference is quite large and has great robustness against finite-key effects. Therefore, our work is meaningful for the real-life applications of quantum secret sharing.<\/jats:p>","DOI":"10.3390\/e23060716","type":"journal-article","created":{"date-parts":[[2021,6,4]],"date-time":"2021-06-04T11:12:13Z","timestamp":1622805133000},"page":"716","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Differential Phase Shift Quantum Secret Sharing Using a Twin Field with Asymmetric Source Intensities"],"prefix":"10.3390","volume":"23","author":[{"given":"Zhao-Ying","family":"Jia","sequence":"first","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Gu","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing-Hong","family":"Li","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7718-0818","authenticated-orcid":false,"given":"Hua-Lei","family":"Yin","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeng-Bing","family":"Chen","sequence":"additional","affiliation":[{"name":"National Laboratory of Solid State Microstructures, School of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,4]]},"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. 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