{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:02:20Z","timestamp":1760238140630,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,18]],"date-time":"2022-06-18T00:00:00Z","timestamp":1655510400000},"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":["61801385","221628","2020JQ-602"],"award-info":[{"award-number":["61801385","221628","2020JQ-602"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["61801385","221628","2020JQ-602"],"award-info":[{"award-number":["61801385","221628","2020JQ-602"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Basic Research Plan in Shaanxi Province of China","award":["61801385","221628","2020JQ-602"],"award-info":[{"award-number":["61801385","221628","2020JQ-602"]}]},{"name":"Foundation of Shaanxi Province Education Department","award":["61801385","221628","2020JQ-602"],"award-info":[{"award-number":["61801385","221628","2020JQ-602"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum digital signatures (QDS) are able to verify the authenticity and integrity of a message in modern communication. However, the current QDS protocols are restricted by the fundamental rate-loss bound and the secure signature distance cannot be further improved. We propose a twin-field quantum digital signature (TF-QDS) protocol with fully discrete phase randomization and investigate its performance under the two-intensity decoy-state setting. For better performance, we optimize intensities of the signal state and the decoy state for each given distance. Numerical simulation results show that our TF-QDS with as few as six discrete random phases can give a higher signature rate and a longer secure transmission distance compared with current quantum digital signatures (QDSs), such as BB84-QDS and measurement-device-independent QDS (MDI-QDS). Moreover, we provide a clear comparison among some possible TF-QDSs constructed by different twin-field key generation protocols (TF-KGPs) and find that the proposed TF-QDS exhibits the best performance. Conclusively, the advantages of the proposed TF-QDS protocol in signature rate and secure transmission distance are mainly due to the single-photon interference applied in the measurement module and precise matching of discrete phases. Besides, our TF-QDS shows the feasibility of experimental implementation with current devices in practical QDS system.<\/jats:p>","DOI":"10.3390\/e24060839","type":"journal-article","created":{"date-parts":[[2022,6,18]],"date-time":"2022-06-18T09:51:11Z","timestamp":1655545871000},"page":"839","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Twin-Field Quantum Digital Signature with Fully Discrete Phase Randomization"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6749-7192","authenticated-orcid":false,"given":"Jiayao","family":"Wu","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Northwest University, Xi\u2019an 710127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"He","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Northwest University, Xi\u2019an 710127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiahui","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Northwest University, Xi\u2019an 710127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaopeng","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Northwest University, Xi\u2019an 710127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minghui","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Northwest University, Xi\u2019an 710127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Simmons, G.J. 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