{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T08:17:16Z","timestamp":1773735436748,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,19]],"date-time":"2021-12-19T00:00:00Z","timestamp":1639872000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ying Guo","award":["61871407,61572529"],"award-info":[{"award-number":["61871407,61572529"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We perform security analysis of a passive continuous-variable quantum key distribution (CV-QKD) protocol by considering the finite-size effect. In the passive CV-QKD scheme, Alice utilizes thermal sources to passively make preparation of quantum state without Gaussian modulations. With this technique, the quantum states can be prepared precisely to match the high transmission rate. Here, both asymptotic regime and finite-size regime are considered to make a comparison. In the finite-size scenario, we illustrate the passive CV-QKD protocol against collective attacks. Simulation results show that the performance of passive CV-QKD protocol in the finite-size case is more pessimistic than that achieved in the asymptotic case, which indicates that the finite-size effect has a great influence on the performance of the single-mode passive CV-QKD protocol. However, we can still obtain a reasonable performance in the finite-size regime by enhancing the average photon number of the thermal state.<\/jats:p>","DOI":"10.3390\/e23121698","type":"journal-article","created":{"date-parts":[[2021,12,19]],"date-time":"2021-12-19T20:37:27Z","timestamp":1639946247000},"page":"1698","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Security Analysis of a Passive Continuous-Variable Quantum Key Distribution by Considering Finite-Size Effect"],"prefix":"10.3390","volume":"23","author":[{"given":"Shengjie","family":"Xu","sequence":"first","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"},{"name":"School of Economics and Mangement, Beihua University, Jilin 132013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yijun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaodong","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9306-2061","authenticated-orcid":false,"given":"Ying","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,19]]},"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":"1012","DOI":"10.1364\/AOP.361502","article-title":"Advances in quantum cryptography","volume":"12","author":"Pirandola","year":"2020","journal-title":"Adv. Opt. Photon."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"025002","DOI":"10.1103\/RevModPhys.92.025002","article-title":"Secure quantum key distribution with realistic devices","volume":"92","author":"Xu","year":"2020","journal-title":"Rev. Mod. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"100501","DOI":"10.1103\/PhysRevLett.114.100501","article-title":"Entanglement swapping between discrete and continuous variables","volume":"114","author":"Takeda","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"020101","DOI":"10.1103\/PhysRevA.94.020101","article-title":"Efficient entanglement criteria for discrete, continuous, and hybrid variables","volume":"94","author":"Gessner","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_7","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_8","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_9","doi-asserted-by":"crossref","first-page":"41501","DOI":"10.1007\/s11467-019-0881-8","article-title":"Plug-and-play dual-phase-modulated continuous-variable quantum key distribution with photon subtraction","volume":"14","author":"Wu","year":"2019","journal-title":"Front. Phys."},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"190503","DOI":"10.1103\/PhysRevLett.97.190503","article-title":"Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution","volume":"97","author":"Cerf","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"190502","DOI":"10.1103\/PhysRevLett.97.190502","article-title":"Optimality of Gaussian attacks in continuous-variable quantum cryptography","volume":"97","author":"Grosshans","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"042305","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_14","doi-asserted-by":"crossref","first-page":"200504","DOI":"10.1103\/PhysRevLett.101.200504","article-title":"Characterization of collective Gaussian attacks and security of coherent-state quantum cryptography","volume":"101","author":"Pirandola","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"110504","DOI":"10.1103\/PhysRevLett.102.110504","article-title":"de Finetti Representation Theorem for Infinite-Dimensional Quantum Systems and Applications to Quantum Cryptography","volume":"102","author":"Renner","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","first-page":"110504","article-title":"Finite-size analysis of a continuous-variable quantum key distribution","volume":"102","author":"Leverrier","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"070501","DOI":"10.1103\/PhysRevLett.114.070501","article-title":"Composable security proof for continuous-variable quantum key distribution with coherent states","volume":"114","author":"Leverrier","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"200501","DOI":"10.1103\/PhysRevLett.118.200501","article-title":"Security of continuous-variable quantum key distribution via a Gaussian de Finetti reduction","volume":"118","author":"Leverrier","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","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. Photon."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"19201","DOI":"10.1038\/srep19201","article-title":"Long-distance continuous-variable quantum key distribution by controlling excess noise","volume":"6","author":"Huang","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3511","DOI":"10.1364\/OL.41.003511","article-title":"Field demonstration of a continuous-variable quantum key distribution network","volume":"41","author":"Huang","year":"2016","journal-title":"Opt. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"010502","DOI":"10.1103\/PhysRevLett.125.010502","article-title":"Long-distance continuous-variable quantum key distribution over 202.81 km of fiber","volume":"125","author":"Zhang","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"032309","DOI":"10.1103\/PhysRevA.86.032309","article-title":"Analysis of imperfections in practical continuous-variable quantum key distribution","volume":"86","author":"Jouguet","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1038\/s41566-019-0504-5","article-title":"An integrated silicon photonic chip platform for continuous-variable quantum key distribution","volume":"13","author":"Zhang","year":"2019","journal-title":"Nat. Photon."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"11254","DOI":"10.1364\/OE.25.011254","article-title":"High speed ultra-broadband amplitude modulators with ultrahigh extinction> 65 dB","volume":"25","author":"Liu","year":"2017","journal-title":"Opt. Express"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"012317","DOI":"10.1103\/PhysRevA.97.012317","article-title":"Passive state preparation in the Gaussian-modulated coherent-states quantum key distribution","volume":"97","author":"Qi","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"022301","DOI":"10.1103\/PhysRevA.101.022301","article-title":"Passive continuous-variable quantum secret sharing using a thermal source","volume":"101","author":"Wu","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"135502","DOI":"10.1088\/1361-6455\/ab0b2a","article-title":"Passive-state preparation in continuous-variable measurement-device-independent quantum key distribution","volume":"52","author":"Bai","year":"2019","journal-title":"J. Phys. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1007\/s11128-019-2486-0","article-title":"Security analysis of passive measurement-device-independent continuous-variable quantum key distribution with almost no public communication","volume":"18","author":"Wu","year":"2019","journal-title":"Quantum Inf. Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"054065","DOI":"10.1103\/PhysRevApplied.13.054065","article-title":"Experimental passive-state preparation for continuous-variable quantum communications","volume":"13","author":"Qi","year":"2020","journal-title":"Phys. Rev. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"032604","DOI":"10.1103\/PhysRevA.103.032604","article-title":"Passive continuous-variable quantum key distribution using a locally generated local oscillator","volume":"103","author":"Wu","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_32","first-page":"643","article-title":"Analysis of the Quantum Algorithm based on Entanglement Measure for Classifying Boolean Multivariate Function into Novel Hidden Classes: Revisited","volume":"15","author":"Zidan","year":"2021","journal-title":"Appl. Math."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"102549","DOI":"10.1016\/j.rinp.2019.102549","article-title":"A quantum algorithm based on entanglement measure for classifying Boolean multivariate function into novel hidden classes","volume":"15","author":"Zidan","year":"2019","journal-title":"Results Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1792","DOI":"10.1016\/j.physe.2011.06.013","article-title":"The quantum computational speed of a single Cooper-pair box","volume":"43","author":"Obada","year":"2011","journal-title":"Phys. E Low Dimens. Syst. Nanostruct."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"130306","DOI":"10.1007\/s11467-017-0717-3","article-title":"Robust general N user authentication scheme in a centralized quantum communication network via generalized GHZ states","volume":"13","author":"Farouk","year":"2018","journal-title":"Front. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"114014","DOI":"10.1088\/0953-4075\/42\/11\/114014","article-title":"Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers","volume":"42","author":"Fossier","year":"2009","journal-title":"J. Phys. B"},{"key":"ref_37","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_38","doi-asserted-by":"crossref","first-page":"043027","DOI":"10.1088\/1367-2630\/17\/4\/043027","article-title":"Coexistence of continuous variable QKD with intense DWDM classical channels","volume":"17","author":"Kumar","year":"2015","journal-title":"New J. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"15043","DOI":"10.1038\/ncomms15043","article-title":"Fundamental limits of repeaterless quantum communications","volume":"8","author":"Pirandola","year":"2017","journal-title":"Nat. Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/12\/1698\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:51:48Z","timestamp":1760169108000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/12\/1698"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,19]]},"references-count":39,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["e23121698"],"URL":"https:\/\/doi.org\/10.3390\/e23121698","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,19]]}}}