{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T07:14:15Z","timestamp":1760426055919,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,20]],"date-time":"2022-02-20T00:00:00Z","timestamp":1645315200000},"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>Quantum key distribution constellation is the key to achieve global quantum networking. However, the networking feasibility of quantum constellation that combines satellite-to-ground accesses selection and inter-satellite routing is faced with a lack of research. In this paper, satellite-to-ground accesses selection is modeled as problems to find the longest paths in directed acyclic graphs. The inter-satellite routing is interpreted as problems to find a maximum flow in graph theory. As far as we know, the above problems are initially understood from the perspective of graph theory. Corresponding algorithms to solve the problems are provided. Although the classical discrete variable quantum key distribution protocol, i.e., BB84 protocol, is applied in simulation, the methods proposed in our paper can also be used to solve other secure key distributions. The simulation results of a low-Earth-orbit constellation scenario show that the Sun is the leading factor in restricting the networking. Due to the solar influence, inter-planar links block the network periodically and, thus, the inter-continental delivery of keys is restricted significantly.<\/jats:p>","DOI":"10.3390\/e24020298","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T08:18:05Z","timestamp":1645431485000},"page":"298","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Networking Feasibility of Quantum Key Distribution Constellation Networks"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9192-9859","authenticated-orcid":false,"given":"Junyong","family":"Wang","sequence":"first","affiliation":[{"name":"Innovation Academy for Microsatellites, Chinese Academy of Sciences, Shanghai 201203, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Liang","family":"Chang","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites, Chinese Academy of Sciences, Shanghai 201203, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Hongyu","family":"Chen","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites, Chinese Academy of Sciences, Shanghai 201203, China"},{"name":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}]},{"given":"Zhencai","family":"Zhu","sequence":"additional","affiliation":[{"name":"Innovation Academy for Microsatellites, Chinese Academy of Sciences, Shanghai 201203, China"},{"name":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s11047-014-9453-6","article-title":"Quantum Cryptography II: How to re-use a one-time pad safely even if P=NP","volume":"13","author":"Bennett","year":"2014","journal-title":"Nat. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1088\/1367-2630\/4\/1\/346","article-title":"Building the quantum network","volume":"4","author":"Elliott","year":"2002","journal-title":"New J. Phys."},{"key":"ref_3","first-page":"138","article-title":"Current status of the DARPA quantum network","volume":"5815","author":"Elliott","year":"2005","journal-title":"Def. Secur."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dianati, M., and Alleaume, R. (2007, January 2\u20136). Architecture of the Secoqc Quantum Key Distribution network. Proceedings of the 2007 First International Conference on Quantum, Nano, and Micro Technologies (ICQNM\u201907), Guadeloupe, France.","DOI":"10.1109\/ICQNM.2007.3"},{"key":"ref_5","unstructured":"All\u00e9aume, R., Bouda, J., Branciard, C., Debuisschert, T., Dianati, M., Gisin, N., Godfrey, M., Grangier, P., L\u00e4nger, T., and Leverrier, A. (2007). SECOQC White Paper on Quantum Key Distribution and Cryptography. arXiv."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1038\/nature23655","article-title":"Satellite-to-ground quantum key distribution","volume":"549","author":"Liao","year":"2017","journal-title":"Nature"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"030501","DOI":"10.1103\/PhysRevLett.120.030501","article-title":"Satellite-Relayed Intercontinental Quantum Network","volume":"120","author":"Liao","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"032309","DOI":"10.1103\/PhysRevA.76.032309","article-title":"Nonunity gain minimal-disturbance measurement","volume":"76","author":"Sabuncu","year":"2007","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"012325","DOI":"10.1103\/PhysRevA.81.012325","article-title":"Environmental Assisted Quantum Information Correction for Continuous Variables","volume":"81","author":"Sabuncu","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.actaastro.2020.02.010","article-title":"Modelling of satellite constellations for trusted node QKD networks","volume":"173","author":"Vergoossen","year":"2020","journal-title":"Acta Astronaut."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1140\/epjqt\/s40507-020-0079-6","article-title":"Scheduling of space to ground quantum key distribution","volume":"7","author":"Polnik","year":"2020","journal-title":"EPJ Quantum Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.actaastro.2020.12.039","article-title":"Modeling research of satellite-to-ground quantum key distribution constellations","volume":"180","author":"Wang","year":"2021","journal-title":"Acta Astronaut."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Tanizawa, Y., Takahashi, R., and Dixon, A. (2016, January 5\u20138). A routing method designed for a Quantum Key Distribution network. Proceedings of the 2016 Eighth International Conference on Ubiquitous and Future Networks (ICUFN), Vienna, Austria.","DOI":"10.1109\/ICUFN.2016.7537018"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1109\/CC.2018.8300270","article-title":"Quantum key distribution network: Optimal secret-key-aware routing method for trust relaying","volume":"15","author":"Yang","year":"2018","journal-title":"China Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1049\/cje.2018.01.013","article-title":"Security Analysis of Stochastic Routing Scheme in Grid-Shaped Partially-Trusted Relay Quantum Key Distribution Network","volume":"27","author":"Liu","year":"2018","journal-title":"Chin. J. Electron."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, Y., Zhao, Y., Chen, W., Dong, K., Yu, X., and Zhang, J. (2020, January 15\u201319). Routing and Key Resource Allocation in SDN-based Quantum Satellite Networks. Proceedings of the 2020 International Wireless Communications and Mobile Computing (IWCMC), Limassol, Cyprus.","DOI":"10.1109\/IWCMC48107.2020.9148563"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1038\/s41534-020-00336-4","article-title":"Feasibility of satellite-to-ground continuous-variable quantum key distribution","volume":"7","author":"Dequal","year":"2021","journal-title":"npj Quantum Inf."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Derkach, I., and Usenko, V.C. (2021). Applicability of Squeezed- and Coherent-State Continuous-Variable Quantum Key Distribution over Satellite Links. Entropy, 23.","DOI":"10.3390\/e23010055"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"012326","DOI":"10.1103\/PhysRevA.72.012326","article-title":"Practical decoy state for quantum key distribution","volume":"72","author":"Ma","year":"2005","journal-title":"Phys. Rev. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"052305","DOI":"10.1103\/PhysRevA.86.052305","article-title":"Statistical fluctuation analysis for measurement-device-independent quantum key distribution","volume":"86","author":"Ma","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"020301","DOI":"10.1088\/1674-1056\/ab5efd","article-title":"Performance analysis of continuous-variable measurementdevice-independent quantum key distribution under diverse weather conditions","volume":"29","author":"Zhang","year":"2020","journal-title":"Chin. Phys. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1038\/nphoton.2017.116","article-title":"Long-distance free-space quantum key distribution in daylight towards inter-satellite communication","volume":"11","author":"Liao","year":"2017","journal-title":"Nat. Photonics"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wertz, J.R. (1978). Spacecraft Attitude Determination and Control, Springer.","DOI":"10.1007\/978-94-009-9907-7"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"012333","DOI":"10.1103\/PhysRevA.95.012333","article-title":"Improved key-rate bounds for practical decoy-state quantum-key-distribution systems","volume":"95","author":"Zhang","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"052333","DOI":"10.1103\/PhysRevA.89.052333","article-title":"Protocol choice and parameter optimization in decoy-state measurementdevice-independent quantum key distribution","volume":"89","author":"Xu","year":"2014","journal-title":"Phys. Rev. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1007\/s11128-017-1687-7","article-title":"Parameter optimization in biased decoy-state quantum key distribution with both source errors and statistical fluctuations","volume":"16","author":"Zhu","year":"2017","journal-title":"Quantum Inf. Process."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/298\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:23:33Z","timestamp":1760135013000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/298"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,20]]},"references-count":26,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["e24020298"],"URL":"https:\/\/doi.org\/10.3390\/e24020298","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,2,20]]}}}