{"id":139907,"date":"2022-05-28T11:23:47","date_gmt":"2022-05-28T16:23:47","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2022\/05\/neural-network-based-prediction-of-the-secret-key-rate-of-quantum-key-distribution"},"modified":"2022-05-28T11:23:47","modified_gmt":"2022-05-28T16:23:47","slug":"neural-network-based-prediction-of-the-secret-key-rate-of-quantum-key-distribution","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2022\/05\/neural-network-based-prediction-of-the-secret-key-rate-of-quantum-key-distribution","title":{"rendered":"Neural network-based prediction of the secret-key rate of quantum key distribution"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/neural-network-based-prediction-of-the-secret-key-rate-of-quantum-key-distribution2.jpg\"><\/a><\/p>\n<p>For instance, continuous-variable (CV) QKD has its own distinct advantages at a metropolitan distance<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 36\" title=\"Pirandola, S. et al. Advances in quantum cryptography. Adv. Opt. Photon. 12, 1012&ndash;1236 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR36\" id=\"ref-link-section-d196726540e519\">36<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 37\" title=\"Zhang, Y. et al. Long-distance continuous-variable quantum key distribution over 202.81 km of fiber. Phys. Rev. Lett. 125, 010502 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR37\" id=\"ref-link-section-d196726540e522\">37<\/a><\/sup> due to the use of common components of coherent optical communication technology. In addition, the homodyne<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 38\" title=\"Grosshans, F. & Grangier, P. Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR38\" id=\"ref-link-section-d196726540e526\">38<\/a><\/sup> or heterodyne<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 39\" title=\"Weedbrook, C. et al. Quantum cryptography without switching. Phys. Rev. Lett. 93, 170504 (2004).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR39\" id=\"ref-link-section-d196726540e530\">39<\/a><\/sup> measurements used by CV-QKD have inherent extraordinary spectral filtering capabilities, which allows the crosstalk in wavelength division multiplexing (WDM) channels to be effectively suppressed. Therefore, hundreds of QKD channels may be integrated into a single optical fiber and can be cotransmitted with classic data channels. This allows QKD channels to be more effectively integrated into existing communication networks. In CV-QKD, discrete modulation technology has attracted much attention<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 31\" title=\"Matsuura, T., Maeda, K., Sasaki, T. & Koashi, M. Finite-size security of continuous-variable quantum key distribution with digital signal processing. Nat. Commun. 12,252 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR31\" id=\"ref-link-section-d196726540e534\">31<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Zhao, Y.-B., Heid, M., Rigas, J. & L\u00fctkenhaus, N. Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks. Phys. Rev. A 79, 012307 (2009).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR40\" id=\"ref-link-section-d196726540e537\">40<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Leverrier, A. & Grangier, P. Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation. Phys. Rev. Lett. 102, 180504 (2009).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR41\" id=\"ref-link-section-d196726540e537_1\">41<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Hirano, T. et al. Implementation of continuous-variable quantum key distribution with discrete modulation. Quantum Sci. Tech. 2, 024010 (2017).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR42\" id=\"ref-link-section-d196726540e537_2\">42<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Ghorai, S., Grangier, P., Diamanti, E. & Leverrier, A. Asymptotic security of continuous-variable quantum key distribution with a discrete modulation. Phys. Rev. X 9, 021059 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR43\" id=\"ref-link-section-d196726540e537_3\">43<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Lin, J., Upadhyaya, T. & L\u00fctkenhaus, N. Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution. Phys. Rev. X 9, 041064 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR44\" id=\"ref-link-section-d196726540e537_4\">44<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Lin, J. & L\u00fctkenhaus, N. Trusted detector noise analysis for discrete modulation schemes of continuous-variable quantum key distribution. Phys. Rev. Appl. 14, 064030 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR45\" id=\"ref-link-section-d196726540e537_5\">45<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Liu, W.-B. et al. Homodyne detection quadrature phase shift keying continuous-variable quantum key distribution with high excess noise tolerance. PRX Quantum 2, 040334 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR46\" id=\"ref-link-section-d196726540e537_6\">46<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Upadhyaya, T., van Himbeeck, T., Lin, J. & L\u00fctkenhaus, N. Dimension reduction in quantum key distribution for continuous-and discrete-variable protocols. PRX Quantum 2, 020325 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR47\" id=\"ref-link-section-d196726540e537_7\">47<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Kanitschar, F. & Pacher, C. Tight secure key rates for CV-QKD with 8PSKmodulation. arXiv preprint arXiv:2107.06110 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR48\" id=\"ref-link-section-d196726540e537_8\">48<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Kaur, E., Guha, S. & Wilde, M. M. Asymptotic security of discrete-modulation protocols for continuous-variable quantum key distribution. Phys. Rev. A 103, 012412 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR49\" id=\"ref-link-section-d196726540e537_9\">49<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 50\" title=\"Denys, A., Brown, P. & Leverrier, A. Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation. Quantum 5,540 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR50\" id=\"ref-link-section-d196726540e540\">50<\/a><\/sup> because of its ability to reduce the requirements for modulation devices. However, due to the lack of symmetry, the security proof of discrete modulation CV-QKD also mainly relies on numerical methods<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Ghorai, S., Grangier, P., Diamanti, E. & Leverrier, A. Asymptotic security of continuous-variable quantum key distribution with a discrete modulation. Phys. Rev. X 9, 021059 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR43\" id=\"ref-link-section-d196726540e544\">43<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Lin, J., Upadhyaya, T. & L\u00fctkenhaus, N. Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution. Phys. Rev. X 9, 041064 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR44\" id=\"ref-link-section-d196726540e544_1\">44<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Lin, J. & L\u00fctkenhaus, N. Trusted detector noise analysis for discrete modulation schemes of continuous-variable quantum key distribution. Phys. Rev. Appl. 14, 064030 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR45\" id=\"ref-link-section-d196726540e544_2\">45<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Liu, W.-B. et al. Homodyne detection quadrature phase shift keying continuous-variable quantum key distribution with high excess noise tolerance. PRX Quantum 2, 040334 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR46\" id=\"ref-link-section-d196726540e544_3\">46<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Upadhyaya, T., van Himbeeck, T., Lin, J. & L\u00fctkenhaus, N. Dimension reduction in quantum key distribution for continuous-and discrete-variable protocols. PRX Quantum 2, 020325 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR47\" id=\"ref-link-section-d196726540e544_4\">47<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 48\" title=\"Kanitschar, F. & Pacher, C. Tight secure key rates for CV-QKD with 8PSKmodulation. arXiv preprint arXiv:2107.06110 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR48\" id=\"ref-link-section-d196726540e547\">48<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 51\" title=\"Hu, H., Im, J., Lin, J., L\u00fctkenhaus, N. & Wolkowicz, H. Robust interior point method for quantum key distribution rate computation. arXiv preprint arXiv:2104.03847 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR51\" id=\"ref-link-section-d196726540e550\">51<\/a><\/sup>.<\/p>\n<p>Unfortunately, calculating a secure key rate by numerical methods requires minimizing a convex function over all eavesdropping attacks related with the experimental data<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 52\" title=\"Bunandar, D., Govia, L. C., Krovi, H. & Englund, D. Numerical finite-key analysis of quantum key distribution. npj Quantum Inf. 6,104 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR52\" id=\"ref-link-section-d196726540e557\">52<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 53\" title=\"George, I., Lin, J. & L\u00fctkenhaus, N. Numerical calculations of the finite key rate for general quantum key distribution protocols. Phys. Rev. Res. 3, 013274 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR53\" id=\"ref-link-section-d196726540e560\">53<\/a><\/sup>. The efficiency of this optimization depends on the number of parameters of the QKD protocol. For example, in discrete modulation CV-QKD, the number of parameters is generally \\(1000\u20133000\\) depending on the different choices of cutoff photon numbers<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 44\" title=\"Lin, J., Upadhyaya, T. & L\u00fctkenhaus, N. Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution. Phys. Rev. X 9, 041064 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR44\" id=\"ref-link-section-d196726540e588\">44<\/a><\/sup>. This leads to the corresponding optimization possibly taking minutes or even hours<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 51\" title=\"Hu, H., Im, J., Lin, J., L\u00fctkenhaus, N. & Wolkowicz, H. Robust interior point method for quantum key distribution rate computation. arXiv preprint arXiv:2104.03847 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR51\" id=\"ref-link-section-d196726540e592\">51<\/a><\/sup>. Therefore, it is especially important to develop tools for calculating the key rate that are more efficient than numerical methods.<\/p>\n<p>In this work, we take the homodyne detection discrete-modulated CV-QKD<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 44\" title=\"Lin, J., Upadhyaya, T. & L\u00fctkenhaus, N. Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution. Phys. Rev. X 9, 041064 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR44\" id=\"ref-link-section-d196726540e600\">44<\/a><\/sup> as an example to construct a neural network capable of predicting the secure key rate for the purpose of saving time and resource consumption. We apply our neural network to a test set obtained at different excess noises and distances. Excellent accuracy and time savings are observed after adjusting the hyperparameters. Importantly, the predicted key rates are highly likely to be secure. Note that our method is versatile and can be extended to quickly calculate the complex secure key rates of various other unstructured quantum key distribution protocols. Through some open source deep learning frameworks for on-device inference, such as TensorFlow Lite<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 54\" title=\"Abadi, M. et al. TensorFlow: Large-scale machine learning on heterogeneous systems (2015). https:\/\/www.tensorflow.org\/. Software available from tensorflow.org.\" href=\"https:\/\/www.nature.com\/articles\/s41598-022-12647-x#ref-CR54\" id=\"ref-link-section-d196726540e604\">54<\/a><\/sup>, our model can also be easily deployed on devices at the <i>edge<\/i> of the network, such as mobile devices, embedded Linux or microcontrollers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>For instance, continuous-variable (CV) QKD has its own distinct advantages at a metropolitan distance36,37 due to the use of common components of coherent optical communication technology. In addition, the homodyne38 or heterodyne39 measurements used by CV-QKD have inherent extraordinary spectral filtering capabilities, which allows the crosstalk in wavelength division multiplexing (WDM) channels to be effectively [\u2026]<\/p>\n","protected":false},"author":359,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1617,6,1492],"tags":[],"class_list":["post-139907","post","type-post","status-publish","format-standard","hentry","category-quantum-physics","category-robotics-ai","category-security"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/139907","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/359"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=139907"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/139907\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=139907"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=139907"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=139907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}