{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:15:14Z","timestamp":1760217314957,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,5,7]],"date-time":"2015-05-07T00:00:00Z","timestamp":1430956800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Information security is increasingly important as society migrates to the information age. Classical cryptography widely used nowadays is based on computational complexity, which means that it assumes that solving some particular mathematical problems is hard on a classical computer. With the development of supercomputers and, potentially, quantum computers, classical cryptography has more and more potential risks. Quantum cryptography provides a solution which is based on the Heisenberg uncertainty principle and no-cloning theorem. While BB84-based quantum protocols are only secure when a single photon is used in communication, the three-stage quantum protocol is  multi-photon tolerant. However, existing analyses assume perfect noiseless channels. In this paper, a multi-photon analysis is performed for the three-stage quantum protocol under the collective-rotation noise model. The analysis provides insights into the impact of the noise level on a three-stage quantum cryptography system.<\/jats:p>","DOI":"10.3390\/e17052919","type":"journal-article","created":{"date-parts":[[2015,5,7]],"date-time":"2015-05-07T10:54:29Z","timestamp":1430996069000},"page":"2919-2931","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Three-Stage Quantum Cryptography Protocol under  Collective-Rotation Noise"],"prefix":"10.3390","volume":"17","author":[{"given":"Linsen","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, N308 Engr. Bldg. 1, University of Houston, Houston, TX 77204-4005, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuhua","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, N308 Engr. Bldg. 1, University of Houston, Houston, TX 77204-4005, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,5,7]]},"reference":[{"key":"ref_1","unstructured":"Bennett, H.C., and Brassard, G. (1984, January 10\u201312). Quantum cryptography: Public key distribution and coin tossing, Bangalore, India."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1103\/PhysRevLett.67.661","article-title":"Quantum cryptography based on Bell\u2019s theorem","volume":"67","author":"Ekert","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3121","DOI":"10.1103\/PhysRevLett.68.3121","article-title":"Quantum cryptography using any two nonorthogonal states","volume":"75","author":"Bennett","year":"1992","journal-title":"Phys. Rev. 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