Quantum key distribution over free space optic (FSO) channel using higher order Gaussian beam spatial modes

Quantum key distribution over free space optic (FSO) channel using higher order Gaussian beam spatial modes

Quantum key distribution (QKD) has emerged as a secure solution of secret key distribution utilizing the well established theories of modern physics. Since its introduction in 1984, many interesting and innovative ideas have been proposed for QKD in order to improve the security and efficiency of the scheme keeping in view of its applications and practical implementation. High error rate QKD scheme for long distance communication – the so-called KMB09 protocol – is one such scheme which was designed to achieve longer communication distance in QKD, without compromising its security, by allowing the utilisation of higher dimensional photon states which is not possible with standard BB84 scheme. However the practical implementation of KMB09 protocol has not been presented yet because of its unique design. In this paper, we propose a framework for the practical implementation of QKD system that runs KMB09 protocol in two or more dimensions of photon states. We present the KMB09 based QKD system design and its simulation for practical implementation based on the encoding of secret bits in higher order Gaussian beam spatial modes. The proposed framework is specifically evaluated in terms of efficiency or success rate with two and four dimensions of photon states. We find that the simulation results of the proposed framework are inline with the numerical and analytical results of the same QKD model presented earlier.

___

  • [1] Mosca M. Cybersecurity in an era with quantum computers: will we be ready? IEEE Security & Privacy 2018; 16 (5): 38-41. doi: 10.1109/MSP.2018.3761723
  • [2] Zhou T, Shen J, Li X, Wang C, Shen J. Quantum cryptography for the future internet and the security analysis. Security and Communication Networks 2018; 1: 1-20.
  • [3] Peres A. Quantum Theory: Concepts and Methods. USA: Springer Science & Business Media, 2006. doi: 10.1007/0- 306-47120-5
  • [4] Rivest RL, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 1978; 21 (2): 120-6. doi: 10.1145/359340.359342
  • [5] Shen J, Zhou T, Chen X, Li J, Susilo W. Anonymous and traceable group data sharing in cloud computing. IEEE Transactions on Information Forensics and Security 2017; 13 (4): 912-25. doi: 10.1109/TIFS.2017.2774439
  • [6] ElGamal T. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory 1985; 31 (4): 469-72. doi: 10.1109/TIT.1985.1057074
  • [7] Tseng YM. An efficient two-party identity-based key exchange protocol. Informatica 2007; 18 (1): 125-36. doi: 10.15388/Informatica.2007.168
  • [8] Tang X, Ma L, Mink A, Chang T, Xu H et al. High-speed quantum key distribution systems for optical ber networks in campus and metro areas. In: Quantum Communications and Quantum Imaging VI. International Society for Optics and Photonics; New York, NY, USA; 2008. pp. 70920I. doi: 10.1117/12.793852
  • [9] Wang Q, Wang XB. Simulating of The Measurement-Device Independent Quantum Key Distribution With Phase Randomized General Sources. USA: Nature, 2014. doi: 10.1038/srep04612
  • [10] Rosenberg D, Peterson CG, Harrington JW, Rice PR, Dallmann N et al. Practical long-distance quantum key distribution system using decoy levels. New Journal of Physics 2009; 11 (4): 045009. doi: 10.1088/1367-2630/11/4/045009
  • [11] Hariharan P, Hariharan P. Optical Holography: Principles, Techniques and Applications. Division of Applied Physics. CSIRO. Canberra, ACT, Australia: Cambridge University Press, 1996. doi: 10.1017/CBO9781139174039
  • [12] Gruneisen MT, Miller WA, Dymale RC, Sweiti AM. Holographic generation of complex fields with spatial light modulators: application to quantum key distribution. Applied Optics 2008; 47 (4): A32-A42. doi: 10.1364/AO.47.000A32
  • [13] Magaña-Loaiza OS, Mirhosseini M, Cross RM, Rafsanjani SM, Boyd RW. Hanbury Brown and Twiss interferometry with twisted light. Science Advances 2016; 2 (4): e1501143. doi: 10.1126/sciadv.1501143
  • [14] Islam NT, Lim CC, Cahall C, Kim J, Gauthier DJ. Provably secure and high-rate quantum key distribution with time-bin qudits. Science Advances 2017; 3 (11): e1701491. doi: 10.1126/sciadv.1701491
  • [15] Wang J, Qin X, Jiang Y, Wang X, Chen L et al. Experimental demonstration of polarization encoding quantum key distribution system based on intrinsically stable polarization-modulated units. Optics Express 2016; 24 (8):
  • 8302-8309. doi: 10.1364/OE.24.008302 [16] Mirhosseini M, Magaña-Loaiza OS, O’Sullivan MN, Rodenburg B, Malik M et al. High-dimensional quantum cryptography with twisted light. New Journal of Physics 2015; 17 (3): 033033. doi: 10.1364/FIO.2014.FM4E.4
  • [17] Goodman JW, Lawrence RW. Digital image formation from electronically detected holograms. Applied Physics Letters 1967; 11 (3): 77-79. doi: 10.1063/1.1755043
  • [18] Khan MM, Murphy M, Beige A. High error-rate quantum key distribution for long-distance communication. New Journal of Physics 2009; 11 (6): 063043. doi: 10.1088/1367-2630/11/6/063043
  • [19] Peřinová V, Lukš A. Quantization of Hermite–Gaussian and Laguerre–Gaussian beams and their spatial transformations. Journal of Modern Optics 2006; 53 (5-6): 659-675. doi: 10.1080/09500340500254285
  • [20] Shor PW, Preskill J. Simple proof of security of the BB84 quantum key distribution protocol. Physical Review Letters 2000; 85 (2): 441. doi: 10.1103/PhysRevLett.85.441
  • [21] Kohnle A, Rizzoli A. Interactive simulations for quantum key distribution. European Journal of Physics 2017; 38 (3): 035403. doi: 10.1088/1361-6404/aa62c8
  • [22] Jakobi M, Simon C, Gisin N, Bancal JD, Branciard C et al. Practical private database queries based on a quantumkey-distribution protocol. Physical Review A 2011; 83 (2): 022301. doi: 10.1103/PhysRevA.83.022301
  • [23] Gao F, Qin S, Huang W, Wen Q. Quantum private query: a new kind of practical quantum cryptographic protocol. Science China Physics, Mechanics & Astronomy 2019; 62 (7): 70301. doi: 10.1007/s11433-018-9324-6
  • [24] Mailloux LO, Morris JD, Grimaila MR, Hodson DD, Jacques DR et al. A modeling framework for studying quantum key distribution system implementation nonidealities. IEEE Access 2015; 3: 110-130. doi: 10.1109/ACCESS.2015.2399101
  • [25] Engle RD, Hodson DD, Grimaila MR, Mailloux LO, McLaughlin CV et al. Modeling quantum optical components, pulses and fiber channels using omnet++. In: 2nd OMNeT++ Community Summit; IBM Research - Zurich; Zurich, Switzerland; 2015. pp. 1-20.
  • [26] Archana B, Krithika S. Implementation of BB84 quantum key distribution using OptSim. In: IEEE 2015 2nd International Conference on Electronics and Communication Systems (ICECS) - Karpagam College of Engineering; Coimbatore, Tamil Nadu, India; 2015. pp. 457-460. doi: 10.1109/ECS.2015.7124946
  • [27] Hussain SS, Khan MM, Baig MM, Wang G. Numerical modelling of quantum key distribution system for KMB09 protocol. International Journal of Computer Science and Information Security 2016; 14 (8): 140.
  • [28] Shall S, Monir MS, Rahman MS. Numerical modeling and simulation of quantum key distribution systems under non-ideal conditions. In: IEEE 2017 International Conference on Telecommunications and Photonics (ICTP) - Bangladesh University of Engineering and Technology (BUET); Bangladesh; 2017. pp. 38-42. doi: 10.1109/ICTP.2017.8285898
  • [29] Wang F, Zeng P, Wang X, Gao H, Li F et al. Towards practical high-speed high dimensional quantum key distribution using partial mutual unbiased basis of photon’s orbital angular momentum. arXiv 2018; arXiv:1801.06582.
  • [30] Mao CC, Li J, Zhu JR, Zhang CM, Wang Q. An improved proposal on the practical quantum key distribution with biased basis. Quantum Information Processing 2017; 16 (10): 256. doi: 10.1007/s11128-017-1707-7
  • [31] Bennett CH, Brassard G. Quantum cryptography: public key distribution and coin tossing. Theoretical Computer Science 2014; 560 (1): 7-11. doi.org/10.1016/j.tcs.2014.05.025
  • [32] Bengtsson I. Three ways to look at mutually unbiased bases. AIP Conference Proceedings American Institute of Physics 2007; 889 (1): 40-51. doi: 10.1063/1.2713445
  • [33] Mayers D. Unconditional security in quantum cryptography. Journal of the ACM 2001; 48 (3): 351-406. doi: 10.1145/382780.382781
  • [34] Nielsen MA, Chuang IL. Quantum Computation and Quantum Information. Cambridge, UK: Cambridge University Press, 2002, pp. 558-559. doi: 10.1017/CBO9780511976667
  • [35] Elboukhari M, Azizi A, Azizi M. Implementation of secure key distribution based on quantum cryptography. In: IEEE 2009 International Conference on Multimedia Computing and Systems; Cancun, Mexico; 2009. pp. 361-365. doi: 10.1109/MMCS.2009.5256673
  • [36] Elboukhari M, Azizi M, Azizi A. Quantum key distribution protocols: a survey. International Journal of Universal Computer Science 2010; 1 (2): 1-20.
  • [37] Brierley S. Quantum key distribution highly sensitive to eavesdropping. arXiv 2009; arXiv:0910.2578.
  • [38] Khan MM, Xu J, Beige A. A detailed analysis of kmb09 qkd protocol. International Journal of Computer Science and Information Security 2017; 15 (1): 529.
  • [39] Paschotta R. Gaussian Beams. Encyclopedia of Laser Physics and Technology. USA: Springer, 2011
  • [40] Nicolas A, Veissier L, Giacobino E, Maxein D, Laurat J. Quantum state tomography of orbital angular momentum photonic qubits via a projection-based technique. New Journal of Physics 2015; 17 (3): 033037. doi: 10.1088/1367- 2630/17/3/033037
  • [41] Mafu M, Dudley A, Goyal S, Giovannini D, McLaren M et al. Higher-dimensional orbital-angular-momentumbased quantum key distribution with mutually unbiased bases. Physical Review A 2013; 88 (3): 032305. doi: 10.1103/PhysRevA.88.032305
  • [42] Harriman J, Serati S, Stockley J. Comparison of transmissive and reflective spatial light modulators for optical manipulation applications. In: Proceeding of SPIE 5930, Optical Trapping and Optical Micromanipulation II; San Diego, CA, US; 2005. pp. 59302D. doi: 10.1117/12.619283
  • [43] Dorrah AH, Zamboni-Rached M, Mojahedi M. Experimental demonstration of tunable refractometer based on orbital angular momentum of longitudinally structured light. Light: Science & Applications 2018; 7 (1): 1-2. doi: 10.1038/s41377-018-0034-9
  • [44] Mirhosseini M, Magana-Loaiza OS, Chen C, Rodenburg B, Malik M et al. Rapid generation of light beams carrying orbital angular momentum. Optics Express 2013; 21 (25): 30196-203. doi: 10.1364/OE.21.030196
  • [45] Rosales-Guzmán C, Forbes A. How to Shape Light With Spatial Light Modulators. Bellingham, WA, USA: SPIE Press, 2017. doi: 10.1117/3.2281295
  • [46] Plick WN, Lapkiewicz R, Ramelow S, Zeilinger A. The forgotten quantum number: a short note on the radial modes of Laguerre-Gauss beams. arXiv 2013; arXiv:1306.6517.
  • [47] James DF, Kwiat PG, Munro WJ, White AG. Measurement of qubits. Physical Review A 2005; 64: 052312. doi: 10.1103/PhysRevA.64.052312
  • [48] Ding Y, Bacco D, Dalgaard K, Cai X, Zhou X et al. High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits. NPJ Quantum Information 2017; 3 (1): 1-7. doi: 10.1038/s41534- 017-0026-2
  • [49] Forbes A, Nape I. Quantum mechanics with patterns of light: progress in high dimensional and multidimensional entanglement with structured light. AVS Quantum Science 2019; 1 (1): 011701. doi: 10.1116/1.5112027
  • [50] Fung CH, Tamaki K, Lo HK. Performance of two quantum-key-distribution protocols. Physical Review A 2006; 73 (1): 012337. doi: 10.1155/2018/8214619
  • [51] Wang J, Zhang Q, Tang CJ. Quantum key distribution protocols using entangled state. In: IEEE 2006 International Conference on Computational Intelligence and Security; Guangzhou, China; 2006. pp. 1355-1358.