{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T07:52:14Z","timestamp":1772869934622,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T00:00:00Z","timestamp":1728950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"A*STAR","award":["C230917004"],"award-info":[{"award-number":["C230917004"]}]},{"name":"A*STAR","award":["C230917010"],"award-info":[{"award-number":["C230917010"]}]},{"name":"Q.InC Strategic Research and Translational Thrust","award":["C230917004"],"award-info":[{"award-number":["C230917004"]}]},{"name":"Q.InC Strategic Research and Translational Thrust","award":["C230917010"],"award-info":[{"award-number":["C230917010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The standard way to measure the performance of existing continuous variable quantum key distribution (CVQKD) protocols is by using the achievable secret key rate (SKR) with respect to one parameter while keeping all other parameters constant. However, this atomistic method requires many individual parameter analyses while overlooking the co-dependence of other parameters. In this work, a numerical tool is developed for comparing different CVQKD protocols while taking into account the simultaneous effects of multiple CVQKD parameters on the capability of protocols to produce positive SKRs. Using the transmittance, excess noise, and modulation amplitude parameter space, regions of positive SKR are identified to compare three discrete modulated (DM) CVQKD protocols. The results show that the M-QAM protocol outperforms the M-APSK and M-PSK protocols and that there is a non-linear increase in the capability to produce positive SKRs as the number of coherent states used for a protocol increases. The tool developed is beneficial for choosing the optimum protocol in unstable channels, such as free space, where the transmittance and excess noise fluctuate, providing a more holistic assessment of a protocol\u2019s capability to produce positive SKRs.<\/jats:p>","DOI":"10.3390\/e26100865","type":"journal-article","created":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T11:28:51Z","timestamp":1729078131000},"page":"865","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Mapping Guaranteed Positive Secret Key Rates for Continuous Variable Quantum Key Distribution"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3437-1200","authenticated-orcid":false,"given":"Mikhael T.","family":"Sayat","sequence":"first","affiliation":[{"name":"Department of Physics, Faculty of Science, University of Auckland, Auckland 1010, New Zealand"},{"name":"Department of Quantum Science and Technology, Research School of Physics, Australian National University, Canberra 2601, Australia"},{"name":"Quantum Innovation Centre (Q.InC), Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"},{"name":"Institute of Materials Research and Engineering (IMRE), Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oliver","family":"Thearle","sequence":"additional","affiliation":[{"name":"Department of Quantum Science and Technology, Research School of Physics, Australian National University, Canberra 2601, Australia"},{"name":"Sensors and Effectors Division, Defence Science and Technology Group, Adelaide 5111, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1374-8566","authenticated-orcid":false,"given":"Biveen","family":"Shajilal","sequence":"additional","affiliation":[{"name":"Quantum Innovation Centre (Q.InC), Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"},{"name":"Institute of Materials Research and Engineering (IMRE), Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6057-4434","authenticated-orcid":false,"given":"Sebastian P.","family":"Kish","sequence":"additional","affiliation":[{"name":"Data61, Commonwealth Scientific and Industrial Research Organisation, Sydney 2015, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4421-601X","authenticated-orcid":false,"given":"Ping Koy","family":"Lam","sequence":"additional","affiliation":[{"name":"Department of Quantum Science and Technology, Research School of Physics, Australian National University, Canberra 2601, Australia"},{"name":"Quantum Innovation Centre (Q.InC), Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"},{"name":"Institute of Materials Research and Engineering (IMRE), Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5069-319X","authenticated-orcid":false,"given":"Nicholas J.","family":"Rattenbury","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Science, University of Auckland, Auckland 1010, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3233-4000","authenticated-orcid":false,"given":"John E.","family":"Cater","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Canterbury, Christchurch 8041, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,15]]},"reference":[{"key":"ref_1","unstructured":"Bennett, C.H., and Brassard, G. 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