×

Gaussian quadrature inference for multicarrier continuous-variable quantum key distribution. (English) Zbl 07899090

Summary: A multicarrier continuous-variable quantum key distribution (CVQKD) protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. Here, we propose the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution. The GQI framework provides a minimal error estimate of the quadratures of the CV quantum states from the measured noisy subcarrier variables. GQI utilizes the fundamentals of regularization theory and statistical information processing. We characterize GQI for multicarrier CVQKD, and define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We introduce the terms statistical secret key rate and statistical private classical information. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and implementable by standard low-complexity statistical functions.

MSC:

81-XX Quantum theory

References:

[1] Pirandola, S.; Mancini, S.; Lloyd, S.; Braunstein, SL, Continuous-variable quantum cryptography using two-way quantum communication, Nat. Phys., 4, 726-730, 2008 · doi:10.1038/nphys1018
[2] Grosshans, F.; Cerf, NJ; Wenger, J.; Tualle-Brouri, R.; Grangier, P., Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables, Quant. Info. Comput., 3, 535-552, 2003 · Zbl 1152.81725
[3] Navascues, M.; Acin, A., Security bounds for continuous variables quantum key distribution, Phys. Rev. Lett., 94, 020505, 2005 · doi:10.1103/PhysRevLett.94.020505
[4] Gyongyosi, L.; Imre, S.; Nguyen, HV, A survey on quantum channel capacities, IEEE Commun. Surv. Tutor., 99, 1, 2018 · doi:10.1109/COMST.2017.2786748
[5] Gyongyosi, L., Imre, S.: Gaussian quadrature inference for multicarrier continuous-variable quantum key distribution. In: SPIE Quantum Information and Computation XIV, 17-21 Apr 2016. Baltimore, Maryland, USA (2016)
[6] Gyongyosi, L., Imre, S.: Secret key rate proof of multicarrier continuous-variable quantum key distribution. Int. J. Commun. Syst. (Wiley). doi:10.1002/dac.3865 (2018)
[7] Gyongyosi, L., Imre, S.: Multiple Access Multicarrier Continuous-Variable Quantum Key Distribution, Chaos, Solitons and Fractals. Elsevier, New York. doi:10.1016/j.chaos.2018.07.006 (ISSN: 0960-0779) (2018) · Zbl 1415.81017
[8] Grosshans, F., Quantum key distribution using Gaussian-modulated coherent states, Nature, 421, 238-241, 2003 · doi:10.1038/nature01289
[9] Pirandola, S., Garcia-Patron, R., Braunstein, S.L., Lloyd, S.: Phys. Rev. Lett. 102, 050503 (2009)
[10] Pirandola, S., Serafini, A., Lloyd, S.: Phys. Rev. A 79, 052327 (2009)
[11] Pirandola, S., Braunstein, S.L., Lloyd, S.: Phys. Rev. Lett. 101, 200504 (2008)
[12] Weedbrook, C., Pirandola, S., Lloyd, S., Ralph, T.: Phys. Rev. Lett. 105, 110501 (2010)
[13] Weedbrook, C., Pirandola, S., Garcia-Patron, R., Cerf, N.J., Ralph, T., Shapiro, J., Lloyd, S.: Rev. Mod. Phys. 84, 621 (2012)
[14] Shieh, W.; Djordjevic, I., OFDM for Optical Communications, 2010, New York: Elsevier, New York
[15] Gyongyosi, L., Imre, S.: Geometrical Analysis of Physically Allowed Quantum Cloning Transformations for Quantum Cryptography, Information Sciences. Elsevier, New York, pp. 1-23. doi:10.1016/j.ins.2014.07.010 (2014) · Zbl 1355.81069
[16] Jouguet, P., Kunz-Jacques, S., Leverrier, A., Grangier, P., Diamanti, E.: Experimental demonstration of long-distance continuous-variable quantum key distribution. arXiv:1210.6216v1 (2012)
[17] Navascues, M.; Grosshans, F.; Acin, A., Optimality of Gaussian attacks in continuous-variable quantum cryptography, Phys. Rev. Lett., 97, 190502, 2006 · doi:10.1103/PhysRevLett.97.190502
[18] Garcia-Patron, R.; Cerf, NJ, Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution, Phys. Rev. Lett., 97, 190503, 2006 · doi:10.1103/PhysRevLett.97.190503
[19] Grosshans, F., Collective attacks and unconditional security in continuous variable quantum key distribution, Phys. Rev. Lett., 94, 020504, 2005 · doi:10.1103/PhysRevLett.94.020504
[20] Adcock, MRA; Hoyer, P.; Sanders, BC, Limitations on continuous-variable quantum algorithms with Fourier transforms, New J. Phys., 11, 103035, 2009 · doi:10.1088/1367-2630/11/10/103035
[21] Gyongyosi, L., Imre, S.: Proceedings Volume 8997, Advances in Photonics of Quantum Computing, Memory, and Communication VII; 89970C. doi:10.1117/12.2038532 (2014)
[22] Imre, S.; Gyongyosi, L., Advanced Quantum Communications—An Engineering Approach, 2012, New Jersey: Wiley, New Jersey · Zbl 1388.81001 · doi:10.1002/9781118337462
[23] Tse, D.; Viswanath, P., Fundamentals of Wireless Communication, 2005, Cambridge: Cambridge University Press, Cambridge · Zbl 1099.94006 · doi:10.1017/CBO9780511807213
[24] Middlet, D.: An Introduction to Statistical Communication Theory: An IEEE Press Classic Reissue, Hardcover, IEEE (ISBN-10: 0780311787, ISBN-13: 978-0780311787) (1960)
[25] Kay, S., Fundamentals of Statistical Signal Processing, 2013, Upper Saddle River: Prentice Hall, Upper Saddle River
[26] Jahromi, OS, Multirate Statistical Signal Processing, 2007, Berlin: Springer, Berlin · Zbl 1141.94002
[27] Heinzel, G., Rudiger, A., Schilling, R.: Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), including a comprehensive list of window functions and some new at-top windows. http://hdl.handle.net/11858/00-001M-0000-0013-557A-5 (2002)
[28] Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP, Numerical Recipes in C: The Art of Scientific Computing, 1993, Cambridge: Cambridge University Press, Cambridge
[29] Imre, S.; Balazs, F., Quantum Computing and Communications—An Engineering Approach, 283, 2005, New York: Wiley, New York
[30] Petz, D., Quantum Information Theory and Quantum Statistics, 2008, Heidelberg: Springer, Heidelberg · Zbl 1145.81002
[31] Gyongyosi, L., Imre, S.: Long-distance Continuous-Variable Quantum Key Distribution with Advanced Reconciliation of a Gaussian Modulation. In: Proceedings of SPIE Photonics West OPTO 2013 (2013)
[32] Pirandola, S.: Capacities of repeater-assisted quantum communications. arXiv:1601.00966 (2016)
[33] Gyongyosi, L., Imre, S.: Entanglement-Gradient Routing for Quantum Networks. Science Report Nature (2017)
[34] Gyongyosi, L., Imre, S.: Entanglement Availability Differentiation Service for the Quantum Internet. Sci. Rep., Nature doi:10.1038/s41598-018-28801-3 (2018)
[35] Biamonte, J., Quantum Machine Learning, Nature, 549, 195-202, 2017 · doi:10.1038/nature23474
[36] Laudenbach, F., Pacher, C., Fred Fung, C.-H., Poppe, A., Peev, M., Schrenk, B., Hentschel, M., Walther, P., Hubel, H.: Continuous-Variable Quantum Key Distribution with Gaussian Modulation—The Theory of Practical Implementations. Adv. Quantum Technol. 1800011 (2018)
[37] Shor, PW, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A, 52, R2493-R2496, 1995 · doi:10.1103/PhysRevA.52.R2493
[38] Kimble, HJ, The quantum Internet, Nature, 453, 1023-1030, 2008 · doi:10.1038/nature07127
[39] Pirandola, S., Laurenza, R., Ottaviani, C., Banchi, L.: Fundamental limits of repeaterless quantum communications. Nat. Commun. 15043. doi:10.1038/ncomms15043 (2017)
[40] Pirandola, S.; Braunstein, SL; Laurenza, R.; Ottaviani, C.; Cope, TPW; Spedalieri, G.; Banchi, L., Theory of channel simulation and bounds for private communication, Quant. Sci. Technol., 3, 035009, 2018 · doi:10.1088/2058-9565/aac394
[41] Laurenza, R.; Pirandola, S., General bounds for sender-receiver capacities in multipoint quantum communications, Phys. Rev. A, 96, 032318, 2017 · doi:10.1103/PhysRevA.96.032318
[42] Bacsardi, L., On the way to quantum-based satellite communication, IEEE Comm. Mag., 51, 8, 50-55, 2013 · doi:10.1109/MCOM.2013.6576338
[43] Gyongyosi, L., Imre, S.: Low-dimensional reconciliation for continuous-variable quantum key distribution. Appl. Sci. doi:10.3390/app8010087 (ISSN 2076-3417) (2018)
[44] Gyongyosi, L.: Diversity extraction for multicarrier continuous-variable quantum key distribution. In: Proceedings of the 2016 24th European Signal Processing Conference (EUSIPCO 2016) (2016)
[45] Gyongyosi, L., Imre, S.: Eigenchannel decomposition for continuous-variable quantum key distribution. In: Proceedings Volume 9377, Advances in Photonics of Quantum Computing, Memory, and Communication VIII; 937711. doi:10.1117/12.2076532 (2015)
[46] Lloyd, S., Capacity of the noisy quantum channel, Phys. Rev. A, 55, 1613-1622, 1997 · doi:10.1103/PhysRevA.55.1613
[47] Lloyd, S.; Shapiro, JH; Wong, FNC; Kumar, P.; Shahriar, SM; Yuen, HP, Infrastructure for the quantum internet, ACM SIGCOMM Comput. Commun. Rev., 34, 9-20, 2004 · doi:10.1145/1039111.1039118
[48] Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum algorithms for supervised and unsupervised machine learning. arXiv:1307.0411 (2013)
[49] Lloyd, S.; Mohseni, M.; Rebentrost, P., Quantum principal component analysis, Nat. Phys., 10, 631, 2014 · doi:10.1038/nphys3029
[50] Muralidharan, S.; Kim, J.; Lutkenhaus, N.; Lukin, MD; Jiang, L., Ultrafast and fault-tolerant quantum communication across long distances, Phys. Rev. Lett, 112, 250501, 2014 · doi:10.1103/PhysRevLett.112.250501
[51] Kiktenko, EO; Pozhar, NO; Anufriev, MN; Trushechkin, AS; Yunusov, RR; Kurochkin, YV; Lvovsky, AI; Fedorov, AK, Quantum-secured blockchain, Quant. Sci. Technol., 3, 035004, 2018 · doi:10.1088/2058-9565/aabc6b
[52] Gyongyosi, L., Imre, S.: Decentralized Base-graph Routing for the Quantum Internet, Physical Review A. American Physical Society, pp. 10-20 (2018)
[53] Van Meter, R., Quantum Networking, 2014, New York: Wiley, New York · Zbl 1303.81006 · doi:10.1002/9781118648919
[54] Gyongyosi, L., Imre, S.: Singular layer transmission for continuous-variable quantum key distribution. In: IEEE Photonics Conference (IPC) 2014, IEEE. doi:10.1109/IPCon.2014.6995246 (2014)
[55] Gyongyosi, L., Imre, S.: Proc. SPIE 9377. In: Advances in Photonics of Quantum Computing, Memory, and Communication VIII, 9377110. doi:10.1117/12.2076532 (2015)
[56] Gyongyosi, L., Imre, S.: http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2195505 (2015)
[57] Gyongyosi, L., Imre, S.: Adaptive multicarrier quadrature division modulation for long-distance continuous-variable quantum key distribution. In: Proc. SPIE 9123, Quantum Information and Computation XII, 912307. doi:10.1117/12.2050095. From Conference Volume 9123, Quantum Information and Computation XII, Baltimore, Maryland, USA (2014)
[58] Gyongyosi, L., Imre, S.: Adaptive Gaussian Quadrature Detection for Continuous-Variable Quantum Key Distribution, SPIE Photonics WestOPTO 2016 Proceedings. In: Advances in Photonics of Quantum Computing, Memory, and Communication IX, doi:10.1117/12.2211743 (2015)
[59] Wang, K.; Yu, XT; Lu, SL; Gong, YX, Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation, Phys. Rev A, 89, 022329, 2014 · doi:10.1103/PhysRevA.89.022329
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.