{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T21:12:16Z","timestamp":1762809136194,"version":"3.37.3"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003336","name":"Bulgarian National Science Fund","doi-asserted-by":"publisher","award":["\u041a\u041f-06-\u041d37\/1 \/06.12.2019"],"award-info":[{"award-number":["\u041a\u041f-06-\u041d37\/1 \/06.12.2019"]}],"id":[{"id":"10.13039\/501100003336","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s11128-021-03235-5","type":"journal-article","created":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T09:02:50Z","timestamp":1630918970000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Novel encoding\u2013decoding procedure for quantum key distribution"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9911-0757","authenticated-orcid":false,"given":"Georgi","family":"Bebrov","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,6]]},"reference":[{"key":"3235_CR1","unstructured":"Bennett, C., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing, Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, 175-179 (1984)"},{"key":"3235_CR2","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1103\/PhysRevLett.67.661","volume":"67","author":"A Ekert","year":"1991","unstructured":"Ekert, A.: Quantum cryptography based on Bellas theorem. Phys. Rev. Lett. 67, 661 (1991)","journal-title":"Phys. Rev. Lett."},{"key":"3235_CR3","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1103\/PhysRevLett.68.557","volume":"68","author":"C Bennett","year":"1992","unstructured":"Bennett, C., Brassard, G., Mermin, N.: Quantum cryptography without Bellas theorem. Phys. Rev. Lett. 68, 557 (1992)","journal-title":"Phys. Rev. Lett."},{"key":"3235_CR4","doi-asserted-by":"publisher","first-page":"3121","DOI":"10.1103\/PhysRevLett.68.3121","volume":"68","author":"C Bennett","year":"1992","unstructured":"Bennett, C.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121 (1992)","journal-title":"Phys. Rev. Lett."},{"key":"3235_CR5","doi-asserted-by":"publisher","first-page":"037902","DOI":"10.1103\/PhysRevLett.89.037902","volume":"89","author":"K Inoue","year":"2002","unstructured":"Inoue, K., Waks, E., Yamamoto, Y.: Differential phase shift quantum key distribution. Phys. Rev. Lett. 89, 037902 (2002)","journal-title":"Phys. Rev. Lett."},{"key":"3235_CR6","doi-asserted-by":"publisher","first-page":"194108","DOI":"10.1063\/1.2126792","volume":"87","author":"D Stucki","year":"2005","unstructured":"Stucki, D., Brunner, N., Gisin, N., Scarani, V., Zbinden, H.: Fast and simple one-way quantum key distribution. Appl. Phys. Lett. 87, 194108 (2005)","journal-title":"Appl. Phys. Lett."},{"key":"3235_CR7","doi-asserted-by":"publisher","first-page":"032302","DOI":"10.1103\/PhysRevA.65.032302","volume":"65","author":"GL Long","year":"2002","unstructured":"Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)","journal-title":"Phys. Rev. A"},{"key":"3235_CR8","doi-asserted-by":"publisher","first-page":"042317","DOI":"10.1103\/PhysRevA.68.042317","volume":"68","author":"FG Deng","year":"2003","unstructured":"Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)","journal-title":"Phys. Rev. A"},{"key":"3235_CR9","doi-asserted-by":"publisher","first-page":"044305","DOI":"10.1103\/PhysRevA.71.044305","volume":"71","author":"C Wang","year":"2005","unstructured":"Wang, C., Deng, F., Li, Y., Liu, X., Long, G.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)","journal-title":"Phys. Rev. A"},{"key":"3235_CR10","doi-asserted-by":"publisher","first-page":"052319","DOI":"10.1103\/PhysRevA.69.052319","volume":"69","author":"FG Deng","year":"2004","unstructured":"Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)","journal-title":"Phys. Rev. A"},{"key":"3235_CR11","doi-asserted-by":"publisher","first-page":"2944","DOI":"10.1016\/j.physleta.2012.08.032","volume":"376","author":"A Banerjee","year":"2012","unstructured":"Banerjee, A., Pathak, A.: Maximally efficient protocols for direct secure quantum communication. Phys. Lett. A 376, 2944 (2012)","journal-title":"Phys. Lett. A"},{"key":"3235_CR12","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1140\/epjd\/e2010-10189-8","volume":"61","author":"CW Tsai","year":"2011","unstructured":"Tsai, C.W., Hsieh, C.R., Hwang, T.: Dense coding using cluster states and its application on deterministic secure quantum communication. Eur. Phys. J. D 61, 783 (2011)","journal-title":"Eur. Phys. J. D"},{"key":"3235_CR13","first-page":"739","volume":"14","author":"S Hassanpour","year":"2014","unstructured":"Hassanpour, S., Houshmand, M.: Efficient controlled quantum secure direct communication based on GHZ-like states. QIP 14, 739 (2014)","journal-title":"QIP"},{"key":"3235_CR14","first-page":"1","volume":"16","author":"D Joy","year":"2017","unstructured":"Joy, D., Surendran, S., Sabir, M.: Efficient deterministic secure quantum communication protocols using multipartite entangled states. QIP 16, 1 (2017)","journal-title":"QIP"},{"key":"3235_CR15","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1140\/epjb\/e2004-00296-4","volume":"41","author":"F Yan","year":"2004","unstructured":"Yan, F., Zhang, X.: A scheme for secure direct communication using EPR pairs and teleportation. Eur. Phys. J. B 41, 75 (2004)","journal-title":"Eur. Phys. J. B"},{"key":"3235_CR16","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1088\/1009-1963\/14\/5\/006","volume":"14","author":"T Gao","year":"2005","unstructured":"Gao, T., Yan, F., Wang, X.: Controlled quantum teleportation and secure direct communication. Chin. Phys. 14, 893 (2005)","journal-title":"Chin. Phys."},{"key":"3235_CR17","doi-asserted-by":"publisher","first-page":"022338","DOI":"10.1103\/PhysRevA.73.022338","volume":"73","author":"A Zhu","year":"2006","unstructured":"Zhu, A., Xia, Y., Fan, Q., Zhang, S.: Secure direct communication based on secret transmitting order of particles. Phys. Rev. A 73, 022338 (2006)","journal-title":"Phys. Rev. A"},{"key":"3235_CR18","first-page":"2195","volume":"14","author":"A Pathak","year":"2015","unstructured":"Pathak, A.: Efficient protocols for unidirectional and bidirectional controlled deterministic secure quantum communication: Different alternative approaches. QIP 14, 2195 (2015)","journal-title":"QIP"},{"key":"3235_CR19","doi-asserted-by":"publisher","first-page":"3632","DOI":"10.1007\/s10773-018-3876-2","volume":"57","author":"Z Cao","year":"2018","unstructured":"Cao, Z., Li, Y., Peng, J., Chai, G., Zhao, G.: Controlled quantum secure direct communication protocol based on huffman compression coding. Int. J. Theor. Phys. 57, 3632 (2018)","journal-title":"Int. J. Theor. Phys."},{"key":"3235_CR20","doi-asserted-by":"publisher","first-page":"035101","DOI":"10.1088\/0031-8949\/89\/03\/035101","volume":"89","author":"L-H Gong","year":"2014","unstructured":"Gong, L.-H., et al.: A continuous variable quantum deterministic key distribution based on two-mode squeezed states. Phys. Scr. 89, 035101 (2014)","journal-title":"Phys. Scr."},{"key":"3235_CR21","doi-asserted-by":"publisher","first-page":"1800520","DOI":"10.1002\/andp.201800520","volume":"531","author":"N-R Zhou","year":"2019","unstructured":"Zhou, N.-R., Zhu, K.-N., Zou, X.-F.: Multi-party semi-quantum key distribution protocol with four-particle cluster state. Annalen Der Physik 531, 1800520 (2019)","journal-title":"Annalen Der Physik"},{"key":"3235_CR22","unstructured":"Mayers, D., Yao, A.: Quantum cryptography with imperfect apparatus, Proceedings of the 39th Annual Symposium on Foundations of Computer Science(FOCS98) (IEEE Computer Society, Washington, DC, 1998), p. 503 (1998)"},{"key":"3235_CR23","doi-asserted-by":"publisher","first-page":"230501","DOI":"10.1103\/PhysRevLett.98.230501","volume":"98","author":"A Ac\u00edn","year":"2007","unstructured":"Ac\u00edn, A., et al.: Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007)","journal-title":"Phys. Rev. Lett."},{"key":"3235_CR24","doi-asserted-by":"publisher","first-page":"2050","DOI":"10.1126\/science.283.5410.2050","volume":"283","author":"H-K Lo","year":"1999","unstructured":"Lo, H.-K., Chau, H.F.: Unconditional security of quantum key distribution over arbitrarily long distances. Science 283, 2050 (1999)","journal-title":"Science"},{"key":"3235_CR25","doi-asserted-by":"publisher","first-page":"130503","DOI":"10.1103\/PhysRevLett.108.130503","volume":"108","author":"H-K Lo","year":"2012","unstructured":"Lo, H.-K., Curty, M., Qi, B.: Measurement-Device-Independent Quantum Key Distribution. Phys. Rev. Lett. 108, 130503 (2012)","journal-title":"Phys. Rev. Lett."},{"key":"3235_CR26","doi-asserted-by":"publisher","first-page":"052316","DOI":"10.1103\/PhysRevA.94.052316","volume":"94","author":"Y Jo","year":"2016","unstructured":"Jo, Y., Son, W.: Key-rate enhancement using qutrit states for quantum key distribution with askew aligned sources. Phys. Rev. A 94, 052316 (2016)","journal-title":"Phys. Rev. A"},{"key":"3235_CR27","doi-asserted-by":"publisher","first-page":"062301","DOI":"10.1103\/PhysRevA.98.062301","volume":"98","author":"L Dellantonio","year":"2018","unstructured":"Dellantonio, L., S\u00f8rensen, A., Bacco, D.: High-dimensional measurement-device-independent quantum key distribution on two-dimensional subspaces. Phys. Rev. A 98, 062301 (2018)","journal-title":"Phys. Rev. A"},{"key":"3235_CR28","doi-asserted-by":"publisher","first-page":"012333","DOI":"10.1103\/PhysRevA.92.012333","volume":"92","author":"F Xu","year":"2015","unstructured":"Xu, F.: Measurement-device-independent quantum communication with an untrusted source. Phys. Rev. A 92, 012333 (2015)","journal-title":"Phys. Rev. A"},{"key":"3235_CR29","doi-asserted-by":"publisher","first-page":"042328","DOI":"10.1103\/PhysRevA.97.042328","volume":"97","author":"Y Zhao","year":"2018","unstructured":"Zhao, Y., Zhang, Y., Xu, B., Yu, S., Guo, H.: Continuous-variable measurement-device-independent quantum key distribution with virtual photon subtraction. Phys. Rev. A 97, 042328 (2018)","journal-title":"Phys. Rev. A"},{"key":"3235_CR30","doi-asserted-by":"publisher","first-page":"034302","DOI":"10.1103\/PhysRevA.90.034302","volume":"90","author":"C-M Zhang","year":"2014","unstructured":"Zhang, C.-M., et al.: Decoy-state measurement-device-independent quantum key distribution based on the Clauser-Horne-Shimony-Holt inequality. Phys. Rev. A 90, 034302 (2014)","journal-title":"Phys. Rev. A"},{"key":"3235_CR31","doi-asserted-by":"publisher","first-page":"160501","DOI":"10.1103\/PhysRevLett.122.160501","volume":"122","author":"H Liu","year":"2019","unstructured":"Liu, H., et al.: Experimental demonstration of high-rate measurement-device-independent quantum key distribution over asymmetric channels. Phys. Rev. Lett. 122, 160501 (2019)","journal-title":"Phys. Rev. Lett."},{"key":"3235_CR32","doi-asserted-by":"publisher","first-page":"042329","DOI":"10.1103\/PhysRevA.97.042329","volume":"97","author":"H-X Ma","year":"2018","unstructured":"Ma, H.-X., et al.: Continuous-variable measurement-device-independent quantum key distribution with photon subtraction. Phys. Rev. A 97, 042329 (2018)","journal-title":"Phys. Rev. A"},{"key":"3235_CR33","doi-asserted-by":"publisher","first-page":"022313","DOI":"10.1103\/PhysRevA.91.022313","volume":"91","author":"C Zhou","year":"2015","unstructured":"Zhou, C., et al.: Biased decoy-state measurement-device-independent quantum key distribution with finite resources. Phys. Rev. A 91, 022313 (2015)","journal-title":"Phys. Rev. A"},{"key":"3235_CR34","doi-asserted-by":"publisher","first-page":"052325","DOI":"10.1103\/PhysRevA.90.052325","volume":"90","author":"Y-C Zhang","year":"2014","unstructured":"Zhang, Y.-C., Li, Z., Yu, S., Gu, W., Peng, X., Guo, H.: Continuous-variable measurement-device-independent quantum key distribution using squeezed states. Phys. Rev. A 90, 052325 (2014)","journal-title":"Phys. Rev. A"},{"key":"3235_CR35","doi-asserted-by":"publisher","first-page":"022328","DOI":"10.1103\/PhysRevA.94.022328","volume":"94","author":"I Puthoor","year":"2016","unstructured":"Puthoor, I., Amiri, R., Wallden, P., Curty, M., Andersson, E.: Measurement-device-independent quantum digital signatures. Phys. Rev. A 94, 022328 (2016)","journal-title":"Phys. Rev. A"},{"key":"3235_CR36","doi-asserted-by":"publisher","first-page":"052325","DOI":"10.1103\/PhysRevA.99.052325","volume":"99","author":"C-H Zhang","year":"2019","unstructured":"Zhang, C.-H., Zhang, C.-M., Wang, Q.: Efficient passive measurement-device-independent quantum key distribution. Phys. Rev. A 99, 052325 (2019)","journal-title":"Phys. Rev. A"},{"key":"3235_CR37","doi-asserted-by":"publisher","first-page":"012313","DOI":"10.1103\/PhysRevA.97.012313","volume":"97","author":"W-F Cao","year":"2018","unstructured":"Cao, W.-F., et al.: One-sided measurement-device-independent quantum key distribution. Phys. Rev. 97, 012313 (2018)","journal-title":"Phys. Rev."},{"key":"3235_CR38","doi-asserted-by":"publisher","first-page":"042334","DOI":"10.1103\/PhysRevA.90.042334","volume":"90","author":"Y-Z Shan","year":"2014","unstructured":"Shan, Y.-Z., et al.: Measurement-device-independent quantum key distribution with a passive decoy-state method. Phys. Rev. A 90, 042334 (2014)","journal-title":"Phys. Rev. A"},{"key":"3235_CR39","doi-asserted-by":"publisher","first-page":"052303","DOI":"10.1103\/PhysRevA.93.052303","volume":"93","author":"X Yang","year":"2016","unstructured":"Yang, X., et al.: Measurement-device-independent entanglement-based quantum key distribution. Phys. Rev. A 93, 052303 (2016)","journal-title":"Phys. Rev. A"},{"key":"3235_CR40","doi-asserted-by":"publisher","first-page":"012301","DOI":"10.1103\/PhysRevA.89.012301","volume":"89","author":"S Abruzzo","year":"2014","unstructured":"Abruzzo, S., Kampermann, H., Bru\u00df, D.: Measurement-device-independent quantum key distribution with quantum memories. Phys. Rev. A 89, 012301 (2014)","journal-title":"Phys. Rev. A"},{"key":"3235_CR41","doi-asserted-by":"publisher","first-page":"022325","DOI":"10.1103\/PhysRevA.93.022325","volume":"93","author":"Y Wu","year":"2016","unstructured":"Wu, Y., Zhou, J., Gong, X., Guo, Y., Zhang, Z.-M., He, G.: Continuous-variable measurement-device-independent multipartite quantum communication. Phys. Rev. A 93, 022325 (2016)","journal-title":"Phys. Rev. A"},{"key":"3235_CR42","volume-title":"High-Rate","author":"N Islam","year":"2018","unstructured":"Islam, N.: High-Rate. High-Dimensional Quantum Key Distribution Systems. Springer Theses, Springer Nature Switzerland AG (2018)"},{"key":"3235_CR43","doi-asserted-by":"publisher","first-page":"17146","DOI":"10.1038\/lsa.2017.146","volume":"7","author":"M Erhard","year":"2018","unstructured":"Erhard, M., Fickler, R., Krenn, M., Zeilinger, A.: Twisted photons: new quantum perspectives in high dimensions. Light. Sci. Appl. 7, 17146 (2018)","journal-title":"Light. Sci. Appl."},{"key":"3235_CR44","unstructured":"Brassard, G., Salvail, L.: Secret-Key Reconciliation by Public Discussion, Advances in Cryptology - EUROCRYPT 93. EUROCRYPT, : Lecture Notes in Computer Science 765. Springer, Berlin, Heidelberg (1993)"},{"key":"3235_CR45","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1109\/18.476316","volume":"41","author":"Ch Bennett","year":"1995","unstructured":"Bennett, Ch., Brassard, G., Crepeau, C., Maurer, U.: Generalized Privacy Amplification. IEEE Trans. Inf. Theory 41, 1915\u20131923 (1995)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"3235_CR46","doi-asserted-by":"publisher","first-page":"5635","DOI":"10.1103\/PhysRevLett.85.5635","volume":"85","author":"A Cabello","year":"2000","unstructured":"Cabello, A.: Quantum Key Distribution in the Holevo Limit. Phys. Rev. Lett. 85, 5635 (2000)","journal-title":"Phys. Rev. Lett."},{"key":"3235_CR47","unstructured":"Golomb, S.: Shift Register Sequences 24\u201327,(1967)"},{"key":"3235_CR48","unstructured":"Bebrov, G.: Randomness Properties of Key Expanding Function in MDI-QKD - under review"},{"key":"3235_CR49","doi-asserted-by":"crossref","unstructured":"Mehic, M., Niemiec, M., Siljak, H., Voznak, M.: Error reconciliation in quantum key distribution protocols, In: Ulidowski I., Lanese I., Schultz U., Ferreira C. (Eds.) Reversible Computation: extending Horizons of Computing. RC 2020. Lecture Notes in Computer Science 12070, p. 2020. Springer, Cham (2020)","DOI":"10.1007\/978-3-030-47361-7_11"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03235-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-021-03235-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03235-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T12:48:02Z","timestamp":1633438082000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-021-03235-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9]]},"references-count":49,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["3235"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03235-5","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"type":"print","value":"1570-0755"},{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2021,9]]},"assertion":[{"value":"3 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 August 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 September 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"296"}}