{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T12:02:26Z","timestamp":1768564946903,"version":"3.49.0"},"reference-count":41,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,6]],"date-time":"2018-08-06T00:00:00Z","timestamp":1533513600000},"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>The scheme of the self-referenced continuous-variable quantum key distribution (SR CV-QKD) has been experimentally demonstrated. However, because of the finite dynamics of Alice\u2019s amplitude modulator, there will be an extra excess noise that is proportional to the amplitude of the reference pulse, while the maximal transmission distance of this scheme is positively correlated with the amplitude of the reference pulse. Therefore, there is a trade-off between the maximal transmission distance and the amplitude of the reference pulse. In this paper, we propose the scheme of SR CV-QKD with virtual photon subtraction, which not only has no need for the use of a high intensity reference pulse to improve the maximal transmission distance, but also has no demand of adding complex physical operations to the original self-referenced scheme. Compared to the original scheme, our simulation results show that a considerable extension of the maximal transmission distance can be obtained when using a weak reference pulse, especially for one-photon subtraction. We also find that our scheme is sensible with the detector\u2019s electronic noise at reception. A longer maximal transmission distance can be achieved for lower electronic noise. Moreover, our scheme has a better toleration of excess noise compared to the original self-referenced scheme, which implies the advantage of using virtual photon subtraction to increase the maximal tolerable excess noise for distant users. These results suggest that our scheme can make the SR CV-QKD from the laboratory possible for practical metropolitan area application.<\/jats:p>","DOI":"10.3390\/e20080578","type":"journal-article","created":{"date-parts":[[2018,8,7]],"date-time":"2018-08-07T03:44:18Z","timestamp":1533613458000},"page":"578","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Enhancing of Self-Referenced Continuous-Variable Quantum Key Distribution with Virtual Photon Subtraction"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5185-2890","authenticated-orcid":false,"given":"Hai","family":"Zhong","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Central South University, Changsha 410083, China"}]},{"given":"Yijun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Central South University, Changsha 410083, China"}]},{"given":"Xudong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7692-7476","authenticated-orcid":false,"given":"Qin","family":"Liao","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Central South University, Changsha 410083, China"}]},{"given":"Xiaodong","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9306-2061","authenticated-orcid":false,"given":"Ying","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Central South University, Changsha 410083, China"},{"name":"School of IOT Engineering, Taihu University, Wuxi 214064, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,6]]},"reference":[{"key":"ref_1","unstructured":"Bennett, C.H., and Brassard, G. (1984). Quantum cryptography: public key distribution and coin tossing. Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, IEEE Press."},{"key":"ref_2","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_3","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_4","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1038\/nphoton.2014.149","article-title":"Secure Quantum Key Distribution","volume":"8","author":"Lo","year":"2014","journal-title":"Nat. Photonics"},{"key":"ref_5","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_6","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_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2007.04.005","article-title":"Quantum information with gaussian states","volume":"44","author":"Wang","year":"2007","journal-title":"Phys. Rep."},{"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":"080309","DOI":"10.1088\/1674-1056\/25\/8\/080309","article-title":"Quantum hacking of two-way continuous-variable quantum key distribution using Trojan-horse attack","volume":"25","author":"Ma","year":"2016","journal-title":"Chin. Phys. B"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"19429","DOI":"10.1364\/OE.25.019429","article-title":"Monitoring of continuous-variable quantum key distribution system in real environment","volume":"25","author":"Liu","year":"2017","journal-title":"Opt. Express"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"052302","DOI":"10.1103\/PhysRevA.95.052302","article-title":"Robust continuous-variable quantum key distribution against practical attacks","volume":"95","author":"Huang","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"022320","DOI":"10.1103\/PhysRevA.96.022320","article-title":"Entanglement-distillation attack on continuous-variable quantum key distribution in a turbulent atmospheric channel","volume":"96","author":"Guo","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"052326","DOI":"10.1103\/PhysRevA.97.052326","article-title":"Channel-parameter estimation for satellite-to-submarine continuous-variable quantum key distribution","volume":"97","author":"Guo","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1016\/j.physleta.2017.12.011","article-title":"Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier","volume":"382","author":"Guo","year":"2018","journal-title":"Phys. Lett. A"},{"key":"ref_15","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_16","doi-asserted-by":"crossref","first-page":"020505","DOI":"10.1103\/PhysRevLett.94.020505","article-title":"Security bounds for continuous variables quantum key distribution","volume":"94","author":"Navascues","year":"2005","journal-title":"Phys. Rev. Lett."},{"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":"062329","DOI":"10.1103\/PhysRevA.87.062329","article-title":"Quantum hacking of a continuous-variable quantum-key-distribution system using a wavelength attack","volume":"87","author":"Huang","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"052309","DOI":"10.1103\/PhysRevA.87.052309","article-title":"Wavelength attack on practical continuous-variable quantum-key-distribution system with a heterodyne protocol","volume":"87","author":"Ma","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"88990N","DOI":"10.1117\/12.2028543","article-title":"Saturation attack on continuous-variable quantum key distribution system","volume":"8899","author":"Qin","year":"2013","journal-title":"Proc. SPIE"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"062313","DOI":"10.1103\/PhysRevA.87.062313","article-title":"Preventing Calibration Attacks on the Local Oscillator in Continuous-Variable Quantum Key Distribution","volume":"87","author":"Jouguet","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"022339","DOI":"10.1103\/PhysRevA.88.022339","article-title":"Local oscillator fluctuation opens a loophole for Eve in practical continuous-variable quantum-key-distribution systems","volume":"88","author":"Ma","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_23","first-page":"041010","article-title":"Self-Referenced Continuous-Variable Quantum Key Distribution Protocol","volume":"5","author":"Soh","year":"2015","journal-title":"Phys. Rev. X"},{"key":"ref_24","first-page":"041009","article-title":"Generating the Local Oscillator Locally in Continuous-Variable Quantum Key Distribution Based on Coherent Detection","volume":"5","author":"Qi","year":"2015","journal-title":"Phys. Rev. X"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3695","DOI":"10.1364\/OL.40.003695","article-title":"High-speed continuous-variable quantum key distribution without sending a local oscillator","volume":"40","author":"Huang","year":"2015","journal-title":"Opt. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"012316","DOI":"10.1103\/PhysRevA.95.012316","article-title":"Self-coherent phase reference sharing for continuous-variable quantum key distribution","volume":"95","author":"Marie","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"032302","DOI":"10.1103\/PhysRevA.61.032302","article-title":"Improvement on teleportation of continuous variables by photon subtraction via conditional measurement","volume":"61","author":"Kurizki","year":"2000","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"043805","DOI":"10.1103\/PhysRevA.71.043805","article-title":"Nonclassicality of a photon-subtracted Gaussian field","volume":"71","author":"Kim","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"042310","DOI":"10.1103\/PhysRevA.73.042310","article-title":"Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states","volume":"73","author":"Kitagawa","year":"2006","journal-title":"Phys.Rev. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"012328","DOI":"10.1103\/PhysRevA.86.012328","article-title":"Enhancing quantum entanglement by photon addition and subtraction","volume":"86","author":"Shapiro","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"012317","DOI":"10.1103\/PhysRevA.87.012317","article-title":"Performance improvement of continuous-variable quantum key distribution via photon subtraction","volume":"87","author":"Huang","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"032304","DOI":"10.1103\/PhysRevA.95.032304","article-title":"Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction","volume":"95","author":"Guo","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"012310","DOI":"10.1103\/PhysRevA.93.012310","article-title":"Non-Gaussian postselection and virtual photon subtraction in continuous-variable quantum key distribution","volume":"93","author":"Li","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"023015","DOI":"10.1088\/1367-2630\/aaa8c4","article-title":"Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection","volume":"20","author":"Liao","year":"2018","journal-title":"New J. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1007\/s11128-017-1617-8","article-title":"Improvement of two-way continuous-variable quantum key distribution with virtual photon subtraction","volume":"16","author":"Zhao","year":"2017","journal-title":"Quantum Inf. Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"042328","DOI":"10.1103\/PhysRevA.97.042328","article-title":"Continuous-variable measurement-device-independent quantum key distribution with virtual photon subtraction","volume":"97","author":"Zhao","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"071101","DOI":"10.1063\/1.3610677","article-title":"Invited Review Article: Single-photon sources and detectors","volume":"82","author":"Eisaman","year":"2011","journal-title":"Rev. Sci. Instrum."},{"key":"ref_38","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_39","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_40","doi-asserted-by":"crossref","first-page":"080502","DOI":"10.1103\/PhysRevLett.96.080502","article-title":"Extremality of Gaussian Quantum States","volume":"96","author":"Wolf","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_41","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."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/8\/578\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:16:47Z","timestamp":1760195807000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/8\/578"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,6]]},"references-count":41,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["e20080578"],"URL":"https:\/\/doi.org\/10.3390\/e20080578","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,6]]}}}