{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,15]],"date-time":"2026-02-15T08:57:27Z","timestamp":1771145847468,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,14]],"date-time":"2023-04-14T00:00:00Z","timestamp":1681430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key-Area Research and Development Program of Guangdong Province","award":["2018B030325002"],"award-info":[{"award-number":["2018B030325002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Measurement-Device-Independent-Quantum Key Distribution (MDI-QKD) has the advantage of extending the secure transmission distances. The MDI-QKD combined with the Hybrid-Trusted and Untrusted Relay (HTUR) is used to deploy large-scale QKD networks, which effectively saves deployment cost. We propose an improved scheme for the QKD network architecture and cost analysis, which simplifies the number of QKD transmitters and incorporates the quantum key pool (QKP) in the QKD network. We developed a novel Hybrid-QKD-Network-Cost (HQNC) heuristic algorithm to solve the cost optimization problem. Simulations verified that the scheme in this paper could save the cost by over 50 percent and 90 percent, respectively.<\/jats:p>","DOI":"10.3390\/e25040661","type":"journal-article","created":{"date-parts":[[2023,4,14]],"date-time":"2023-04-14T09:23:43Z","timestamp":1681464223000},"page":"661","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Cost-Optimization-Based Quantum Key Distribution over Quantum Key Pool Optical Networks"],"prefix":"10.3390","volume":"25","author":[{"given":"Jie","family":"Jia","sequence":"first","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China"},{"name":"National Quantum Communication (Guangdong) Co., Ltd., Guangzhou 510700, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bowen","family":"Dong","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China"},{"name":"National Quantum Communication (Guangdong) Co., Ltd., Guangzhou 510700, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Le","family":"Kang","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China"},{"name":"National Quantum Communication (Guangdong) Co., Ltd., Guangzhou 510700, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huanwen","family":"Xie","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China"},{"name":"National Quantum Communication (Guangdong) Co., Ltd., Guangzhou 510700, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8855-6350","authenticated-orcid":false,"given":"Banghong","family":"Guo","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,14]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.tcs.2014.05.025","article-title":"Quantum cryptography: Public key distribution and coin tossing","volume":"560","author":"Bennett","year":"2014","journal-title":"Theor. Comput. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1364\/JOSAB.36.000B31","article-title":"Multi-tenant provisioning over software defined networking enabled metropolitan area quantum key distribution networks","volume":"36","author":"Cao","year":"2019","journal-title":"J. Opt. Soc. Am."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2544","DOI":"10.1364\/OE.27.002544","article-title":"Multi-tenant secret-key assignment over quantum key distribution networks","volume":"27","author":"Cao","year":"2019","journal-title":"Opt Express"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"070501","DOI":"10.1103\/PhysRevLett.124.070501","article-title":"Sending-or-Not-Sending with Independent Lasers: Secure Twin-Field Quantum Key Distribution over 509 km","volume":"124","author":"Chen","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1038\/s41586-020-03093-8","article-title":"An integrated space-to-ground quantum communication network over 4,600 kilometres","volume":"589","author":"Chen","year":"2021","journal-title":"Nature"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41534-019-0221-4","article-title":"Cambridge quantum network","volume":"5","author":"Dynes","year":"2019","journal-title":"NPJ Quantum Inf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1103\/RevModPhys.83.33","article-title":"Quantum repeaters based on atomic ensembles and linear optics","volume":"83","author":"Sangouard","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1038\/s41566-019-0468-5","article-title":"Experimental quantum repeater without quantum memory","volume":"13","author":"Li","year":"2019","journal-title":"Nat. Photonics"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/1757-899X\/1076\/1\/012054","article-title":"Performance Analysis of Quantum Repeaters Based Hybrid Communications Networks","volume":"1076","author":"Kadhim","year":"2021","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3530","DOI":"10.1109\/JLT.2022.3153992","article-title":"Secret-Key Provisioning With Collaborative Routing in Partially-Trusted-Relay-based Quantum-Key-Distribution-Secured Optical Networks","volume":"40","author":"Yu","year":"2022","journal-title":"J. Light. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"421","DOI":"10.4028\/www.scientific.net\/AMR.709.421","article-title":"The Trust Relay QKD Network Communication Research","volume":"709","author":"Han","year":"2013","journal-title":"Adv. Mater. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2701","DOI":"10.1109\/JSAC.2021.3064662","article-title":"Hybrid Trusted\/Untrusted Relay-Based Quantum Key Distribution Over Optical Backbone Networks","volume":"39","author":"Cao","year":"2021","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"24884","DOI":"10.1364\/OE.427804","article-title":"Optimizing the deployment of quantum key distribution switch-based networks","volume":"29","author":"Tayduganov","year":"2021","journal-title":"Opt Express"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hua, X., Hu, M., and Guo, B. (2022). Multi-User Measurement-Device-Independent Quantum Key Distribution Based on GHZ Entangled State. Entropy, 24.","DOI":"10.3390\/e24060841"},{"key":"ref_16","first-page":"138","article-title":"Current status of the DARPA quantum network (Invited Paper)","volume":"2005","author":"Donkor","year":"2005","journal-title":"Quantum Inf. Comput. III"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"075001","DOI":"10.1088\/1367-2630\/11\/7\/075001","article-title":"The SECOQC quantum key distribution network in Vienna","volume":"11","author":"Peev","year":"2009","journal-title":"New J. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sasaki, M., Fujiwara, M., Ishizuka, H., Klaus, W., Wakui, K., Takeoka, M., Tanaka, A., Yoshino, K., Nambu, Y., and Takahashi, S. (2011). Field test of quantum key distribution in the Tokyo QKD Network. arXiv.","DOI":"10.1364\/IQEC.2011.I403"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"130503","DOI":"10.1103\/PhysRevLett.108.130503","article-title":"Measurement-device-independent quantum key distribution","volume":"108","author":"Lo","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Valivarthi1, R., Umesh, P., John, C., Owen, K.A., Verma, V.B., Nam, S.W., Oblak, D., Zhou, Q., and Tittel, W. (2019). Measurement-device-independent quantum key distribution coexisting with classical communication. Quantum Sci. Technol., 4, 4.","DOI":"10.1088\/2058-9565\/ab2e62"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3382","DOI":"10.1109\/JLT.2018.2834949","article-title":"Time-Scheduled Quantum Key Distribution (QKD) Over WDM Networks","volume":"36","author":"Cao","year":"2018","journal-title":"J. Light. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"21225","DOI":"10.1364\/OE.425562","article-title":"Multi-path-based quasi-real-time key provisioning in quantum-key-distribution enabled optical networks (QKD-ON)","volume":"29","author":"Yu","year":"2021","journal-title":"Opt. Express"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2661","DOI":"10.1109\/JLT.2021.3056109","article-title":"Key-Size-Driven Wavelength Resource Sharing Scheme for QKD and the Time-Varying Data Services","volume":"39","author":"Niu","year":"2021","journal-title":"J. Light. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"26453","DOI":"10.1364\/OE.25.026453","article-title":"Key on demand (KoD) for software-defined optical networks secured by quantum key distribution (QKD)","volume":"25","author":"Cao","year":"2017","journal-title":"Opt Express"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevX.6.011024","article-title":"Measurement-Device-Independent Quantum Key Distribution over Untrustful Metropolitan Network","volume":"6","author":"Tang","year":"2016","journal-title":"Phys. Rev."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"160501","DOI":"10.1103\/PhysRevLett.122.160501","article-title":"Experimental Demonstration of High-Rate Measurement-Device-Independent Quantum Key Distribution over Asymmetric Channels","volume":"122","author":"Liu","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.optcom.2017.02.028","article-title":"Resource Assignment Strategy in Optical Networks Integrated With Quantum Key Distribution","volume":"9","author":"Cao","year":"2017","journal-title":"J. Opt. Commun. Netw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1364\/JOCN.10.000421","article-title":"Virtual Network Function Deployment and Service Automation to Provide End-to-End Quantum Encryption","volume":"10","author":"Aguado","year":"2018","journal-title":"J. Opt. Commun. Netw."},{"key":"ref_29","unstructured":"(2023, April 07). \u201cUnderstanding Quantum Cryptography,\u201d IDQ White Paper [Online]. Available online: https:\/\/marketing.idquantique.com\/acton\/attachment\/11868\/f-020d\/1\/-\/-\/-\/-\/Understanding%20Quantum%20Cryptography_White%20Paper.pdf."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1364\/JOCN.11.000285","article-title":"Cost-Efficient Quantum Key Distribution (QKD) Over WDM Networks","volume":"11","author":"Cao","year":"2019","journal-title":"J. Opt. Commun. Netw."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"10359","DOI":"10.1364\/OE.23.010359","article-title":"Perspectives and limitations of QKD integration in metropolitan area networks","volume":"23","author":"Aleksic","year":"2015","journal-title":"Opt. Express"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1049\/iet-qtc.2019.0005","article-title":"Quantum key distribution integration with optical dense wavelength division multiplexing: A review","volume":"1","author":"Bahrami","year":"2020","journal-title":"IET Quantum Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/4\/661\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:15:58Z","timestamp":1760123758000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/4\/661"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,14]]},"references-count":32,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["e25040661"],"URL":"https:\/\/doi.org\/10.3390\/e25040661","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,14]]}}}