{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:21:40Z","timestamp":1760235700460,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T00:00:00Z","timestamp":1631836800000},"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":["61971436"],"award-info":[{"award-number":["61971436"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007085","name":"National University of Defense Technology","doi-asserted-by":"publisher","award":["19-QNCXJ"],"award-info":[{"award-number":["19-QNCXJ"]}],"id":[{"id":"10.13039\/501100007085","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Innovative Talents Promotion Plan in Shaanxi Province","award":["2020KJXX-011"],"award-info":[{"award-number":["2020KJXX-011"]}]},{"name":"Key Research and Development Program of Shaanxi","award":["2019ZDLGY09-01"],"award-info":[{"award-number":["2019ZDLGY09-01"]}]},{"name":"Innovative Key Projects Promotion in Information and Communication College","award":["YJKT-ZD-2105"],"award-info":[{"award-number":["YJKT-ZD-2105"]}]},{"name":"Innovative Talents Promotion in Information and Communication College","award":["YJKT-RC-2113"],"award-info":[{"award-number":["YJKT-RC-2113"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Polarization encoding has been extensively used in quantum key distribution (QKD) implementations along free-space links. However, the calculation model to characterize channel transmittance and quantum bit error rate (QBER) for free-space QKD has not been systematically studied. As a result, it is often assumed that misalignment error is equal to a fixed value, which is not theoretically rigorous. In this paper, we investigate the depolarization and rotation of the signal beams resulting from spatially-dependent polarization effects of the use of curved optics in an off-axis configuration, where decoherence can be characterized by the Huygens\u2013Fresnel principle and the cross-spectral density matrix (CSDM). The transmittance and misalignment error in a practical free-space QKD can thus be estimated using the method. Furthermore, the numerical simulations clearly show that the polarization effect caused by turbulence can be effectively mitigated when maintaining good beam coherence properties.<\/jats:p>","DOI":"10.3390\/e23091224","type":"journal-article","created":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T21:23:29Z","timestamp":1631913809000},"page":"1224","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Influence of Source Parameters on the Polarization Properties of Beams for Practical Free-Space Quantum Key Distribution"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9533-3232","authenticated-orcid":false,"given":"Tianyi","family":"Wu","sequence":"first","affiliation":[{"name":"Information and Communication College, National University of Defense Technology, Xi\u2019an 710006, China"}]},{"given":"Qing","family":"Pan","sequence":"additional","affiliation":[{"name":"Information and Communication College, National University of Defense Technology, Xi\u2019an 710006, China"}]},{"given":"Chushan","family":"Lin","sequence":"additional","affiliation":[{"name":"Information and Communication College, National University of Defense Technology, Xi\u2019an 710006, China"}]},{"given":"Lei","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Information and Navigation, Air Force Engineering University, Xi\u2019an 710077, China"}]},{"given":"Shanghong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Information and Navigation, Air Force Engineering University, Xi\u2019an 710077, China"}]},{"given":"Yijun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Information and Communication College, National University of Defense Technology, Xi\u2019an 710006, China"},{"name":"Graduate Institute, Rocket Force University of Engineering, Xi\u2019an 710025, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1471-8668","authenticated-orcid":false,"given":"Xingyu","family":"Wang","sequence":"additional","affiliation":[{"name":"Information and Communication College, National University of Defense Technology, Xi\u2019an 710006, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2745-0258","authenticated-orcid":false,"given":"Chen","family":"Dong","sequence":"additional","affiliation":[{"name":"Information and Communication College, National University of Defense Technology, Xi\u2019an 710006, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2050","DOI":"10.1126\/science.283.5410.2050","article-title":"Unconditional security of quantum key distribution over arbitrarily long distances","volume":"283","author":"Lo","year":"1999","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1103\/PhysRevLett.68.557","article-title":"Quantum cryptography without Bell\u2019s theorem","volume":"68","author":"Bennett","year":"1992","journal-title":"Phys. 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