{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:57:30Z","timestamp":1760241450932,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T00:00:00Z","timestamp":1519862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Project of the Ministry of Science and Technology of China","award":["2016YFA0301403"],"award-info":[{"award-number":["2016YFA0301403"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11504219","61378010"],"award-info":[{"award-number":["11504219","61378010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanxi 1331KSC"},{"name":"Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study the equivalence between the entanglement-based scheme and prepare-and-measure scheme of unidimensional (UD) continuous-variable quantum key distribution protocol. Based on this equivalence, the physicality and security of the UD coherent-state protocols in the ideal detection and realistic detection conditions are investigated using the Heisenberg uncertainty relation, respectively. We also present a method to increase both the secret key rates and maximal transmission distances of the UD coherent-state protocol by adding an optimal noise to the reconciliation side. It is expected that our analysis will aid in the practical applications of the UD protocol.<\/jats:p>","DOI":"10.3390\/e20030157","type":"journal-article","created":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T12:15:44Z","timestamp":1519906544000},"page":"157","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Security Analysis of Unidimensional Continuous-Variable Quantum Key Distribution Using Uncertainty Relations"],"prefix":"10.3390","volume":"20","author":[{"given":"Pu","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0055-0929","authenticated-orcid":false,"given":"Xuyang","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China"},{"name":"Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0228-7693","authenticated-orcid":false,"given":"Yongmin","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China"},{"name":"Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1103\/RevModPhys.74.145","article-title":"Quantum cryptography","volume":"74","author":"Gisin","year":"2002","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1103\/RevModPhys.81.1301","article-title":"The security of practical quantum key distribution","volume":"81","author":"Scarani","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"052311","DOI":"10.1103\/PhysRevA.63.052311","article-title":"Quantum distribution of gaussian keys using squeezed states","volume":"63","author":"Cerf","year":"2001","journal-title":"Phys. Rev. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"167901","DOI":"10.1103\/PhysRevLett.89.167901","article-title":"Continuous variable quantum cryptography: Beating the 3 db loss limit","volume":"89","author":"Silberhorn","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"170504","DOI":"10.1103\/PhysRevLett.93.170504","article-title":"Quantum cryptography without switching","volume":"93","author":"Weedbrook","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"045023","DOI":"10.1088\/1367-2630\/11\/4\/045023","article-title":"Field test of a continuous-variable quantum key distribution prototype","volume":"11","author":"Fossier","year":"2009","journal-title":"New J. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"042312","DOI":"10.1103\/PhysRevA.83.042312","article-title":"Continuous-variable quantum-key-distribution protocols with a non-gaussian modulation","volume":"83","author":"Leverrier","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1038\/ncomms2097","article-title":"Continuous variable quantum key distribution with modulated entangled states","volume":"3","author":"Madsen","year":"2012","journal-title":"Nat. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"124202","DOI":"10.1088\/0256-307X\/29\/12\/124202","article-title":"Ultrastable fiber-based time-domain balanced homodyne detector for quantum communication","volume":"29","author":"Wang","year":"2012","journal-title":"Chin. Phys. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1103\/RevModPhys.84.621","article-title":"Gaussian quantum information","volume":"84","author":"Weedbrook","year":"2012","journal-title":"Rev. Mod. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"010305","DOI":"10.1088\/0256-307X\/30\/1\/010305","article-title":"Four-state modulation continuous variable quantum key distribution over a 30-km fiber and analysis of excess noise","volume":"30","author":"Wang","year":"2013","journal-title":"Chin. Phys. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8795","DOI":"10.1038\/ncomms9795","article-title":"Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks","volume":"6","author":"Gehring","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Li, Z., Weedbrook, C., Marshall, K., Pirandola, S., Yu, S., and Guo, H. (2015). Noiseless linear amplifiers in entanglement-based continuous-variable quantum key distribution. Entropy, 17.","DOI":"10.3390\/e17074547"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"20481","DOI":"10.1364\/OE.24.020481","article-title":"Practical continuous-variable quantum key distribution without finite sampling bandwidth effects","volume":"24","author":"Li","year":"2016","journal-title":"Opt. Express"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bai, D.Y., Huang, P., Ma, H.X., Wang, T., and Zeng, G.H. (2017). Performance improvement of plug-and-play dual-phase-modulated quantum key distribution by using a noiseless amplifier. Entropy, 19.","DOI":"10.3390\/e19100546"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"044401","DOI":"10.7567\/JJAP.56.044401","article-title":"High-efficiency reconciliation for continuous variable quantum key distribution","volume":"56","author":"Bai","year":"2017","journal-title":"Jpn. J. Appl. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"057902","DOI":"10.1103\/PhysRevLett.88.057902","article-title":"Continuous variable quantum cryptography using coherent states","volume":"88","author":"Grosshans","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1038\/nature01289","article-title":"Quantum key distribution using gaussian-modulated coherent states","volume":"421","author":"Grosshans","year":"2003","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"170502","DOI":"10.1103\/PhysRevLett.93.170502","article-title":"Security of quantum key distribution with coherent states and homodyne detection","volume":"93","author":"Iblisdir","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"020504","DOI":"10.1103\/PhysRevLett.94.020504","article-title":"Collective attacks and unconditional security in continuous variable quantum key distribution","volume":"94","author":"Grosshans","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"180503","DOI":"10.1103\/PhysRevLett.95.180503","article-title":"No-switching quantum key distribution using broadband modulated coherent light","volume":"95","author":"Lance","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"042503","DOI":"10.1103\/PhysRevA.76.042305","article-title":"Quantum key distribution over 25 km with an all-fiber continuous-variable system","volume":"76","author":"Lodewyck","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"052323","DOI":"10.1103\/PhysRevA.76.052323","article-title":"Experimental study on the gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers","volume":"76","author":"Qi","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_24","first-page":"7600308","article-title":"FPGA-based implementation of size-adaptive privacy amplification in quantum key distribution","volume":"9","author":"Yang","year":"2017","journal-title":"Photonics J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1038\/nphoton.2013.63","article-title":"Experimental demonstration of long-distance continuous-variable quantum key distribution","volume":"7","author":"Jouguet","year":"2013","journal-title":"Nat. Photonics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"040303","DOI":"10.1088\/1674-1056\/26\/4\/040303","article-title":"Continuous variable quantum key distribution","volume":"26","author":"Li","year":"2017","journal-title":"Chin. Phys. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"042312","DOI":"10.1103\/PhysRevA.96.042312","article-title":"Imperfect state preparation in continuous-variable quantum key distribution","volume":"96","author":"Liu","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"062337","DOI":"10.1103\/PhysRevA.92.062337","article-title":"Unidimensional continuous-variable quantum key distribution","volume":"92","author":"Usenko","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"062330","DOI":"10.1103\/PhysRevA.95.062330","article-title":"Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution","volume":"95","author":"Wang","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"27995","DOI":"10.1364\/OE.25.027995","article-title":"Finite-size analysis of unidimensional continuous-variable quantum key distribution under realistic conditions","volume":"25","author":"Wang","year":"2017","journal-title":"Opt. Express"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1103\/RevModPhys.77.513","article-title":"Quantum information with continuous variables","volume":"77","author":"Braunstein","year":"2005","journal-title":"Rev. Mod. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1364\/JOSAB.24.000347","article-title":"Detecting entanglement by symplectic uncertainty relations","volume":"24","author":"Serafini","year":"2007","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"535","DOI":"10.26421\/QIC3.s-6","article-title":"Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables","volume":"3","author":"Grosshans","year":"2003","journal-title":"Quantum Inform. Comput."},{"key":"ref_34","unstructured":"Ben-Israel, A., and Greville, T.N.E. (2003). Generalized Inverses: Theory and Applications, Springer. [2nd ed.]."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"R19","DOI":"10.1088\/1464-4266\/7\/4\/R01","article-title":"Quantifying decoherence in continuous variable systems","volume":"7","author":"Serafini","year":"2005","journal-title":"J. Opt. B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"130501","DOI":"10.1103\/PhysRevLett.102.130501","article-title":"Continuous-variable quantum key distribution protocols over noisy channels","volume":"102","author":"Cerf","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Milicevic, M., Feng, C., Zhang, L.M., and Gulak, P.G. (arXiv, 2017). Key reconciliation with low-density parity-check codes for long-distance quantum cryptography, arXiv.","DOI":"10.1038\/s41534-018-0070-6"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/3\/157\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:57:12Z","timestamp":1760194632000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/3\/157"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,1]]},"references-count":37,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,3]]}},"alternative-id":["e20030157"],"URL":"https:\/\/doi.org\/10.3390\/e20030157","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,3,1]]}}}