Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Scalable implementation of (d+1) mutually unbiased bases for d-dimensional quantum key distribution

Takuya Ikuta1,2,*, Seiseki Akibue3,†, Yuya Yonezu1, Toshimori Honjo1, Hiroki Takesue1, and Kyo Inoue2

  • 1NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
  • 2Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan
  • 3NTT Communication Science Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan

  • *takuya.ikuta.xu@hco.ntt.co.jp
  • †seiseki.akibue.rb@hco.ntt.co.jp

Phys. Rev. Research 4, L042007 – Published 12 October, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042007

Abstract

A high-dimensional quantum key distribution (QKD) can improve error rate tolerance and the secret key rate. Many d-dimensional QKDs have used two mutually unbiased bases (MUBs), while (d+1) MUBs enable a more robust QKD, especially against correlated errors. However, a scalable implementation has not been achieved because the setups have required d devices even for two MUBs or a flexible convertor for a specific optical mode. Here, we propose a scalable and general implementation of (d+1) MUBs using logpd interferometers in prime power dimensions d=pN. We implemented the setup for time-bin states and observed an average error rate of 3.8% for phase bases, which is lower than the 23.17% required for a secure QKD against coherent attack in d=4.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (45)

  1. C. H. Bennett and G. Brassard, Quantum Cryptography: Public Key Distribution and Coin Tossing, in Proceedings of IEEE International Conference on Computers Systems and Signal Processing (IEEE, Bangalore, India, 1984), pp. 175–179.
  2. A. K. Ekert, Quantum Cryptography Based on Bell's Theorem, Phys. Rev. Lett. 67, 661 (1991).
  3. D. Bruß, Optimal Eavesdropping in Quantum Cryptography with Six States, Phys. Rev. Lett. 81, 3018 (1998).
  4. D. G. Enzer, P. G. Hadley, R. J. Hughes, C. G. Peterson, and P. G. Kwiat, Entangled-photon six-state quantum cryptography, New J. Phys. 4, 45 (2002).
  5. K. Inoue, E. Waks, and Y. Yamamoto, Differential Phase Shift Quantum Key Distribution, Phys. Rev. Lett. 89, 037902 (2002).
  6. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors, Nat. Photon. 1, 343 (2007).
  7. T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, Experimental Demonstration of Free-Space Decoy-State Quantum Key Distribution over 144 km, Phys. Rev. Lett. 98, 010504 (2007).
  8. H.-K. Lo, M. Curty, and B. Qi, Measurement-Device-Independent Quantum Key Distribution, Phys. Rev. Lett. 108, 130503 (2012).
  9. T. Sasaki, Y. Yamamoto, and M. Koashi, Practical quantum key distribution protocol without monitoring signal disturbance, Nature (London) 509, 475 (2014).
  10. H. Takesue, T. Sasaki, K. Tamaki, and M. Koashi, Experimental quantum key distribution without monitoring signal disturbance, Nat. Photon. 9, 827 (2015).
  11. H.-L. Yin, T.-Y. Chen, Z.-W. Yu, H. Liu, L.-X. You, Y.-H. Zhou, S.-J. Chen, Y. Mao, M.-Q. Huang, W.-J. Zhang, H. Chen, M. J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.-B. Wang, and J.-W. Pan, Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber, Phys. Rev. Lett. 117, 190501 (2016).
  12. S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou et al., Satellite-to-ground quantum key distribution, Nature (London) 549, 43 (2017).
  13. A. Boaron, G. Boso, D. Rusca, C. Vulliez, C. Autebert, M. Caloz, M. Perrenoud, G. Gras, F. Bussières, M.-J. Li, D. Nolan, A. Martin, and H. Zbinden, Secure Quantum Key Distribution over 421 km of Optical Fiber, Phys. Rev. Lett. 121, 190502 (2018).
  14. W. K. Wootters and B. D. Fields, Optimal state-determination by mutually unbiased measurements, Ann. Phys. 191, 363 (1989).
  15. T. Durt, About mutually unbiased bases in even and odd prime power dimensions, J. Phys. A: Math. Gen. 38, 5267 (2005).
  16. T. Durt, B.-G. Englert, I. Bengtsson, and K. Życzkowski, On mutually unbiased bases, Intl. J. Quantum Inf. 08, 535 (2010).
  17. M. Koashi, Simple security proof of quantum key distribution based on complementarity, New J. Phys. 11, 045018 (2009).
  18. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, Security of Quantum Key Distribution Using d-Level Systems, Phys. Rev. Lett. 88, 127902 (2002).
  19. L. Sheridan and V. Scarani, Security proof for quantum key distribution using qudit systems, Phys. Rev. A 82, 030301(R) (2010).
  20. A. Ferenczi and N. Lütkenhaus, Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning, Phys. Rev. A 85, 052310 (2012).
  21. R. Wang, Z.-Q. Yin, H. Liu, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, Tight finite-key analysis for generalized high-dimensional quantum key distribution, Phys. Rev. Res. 3, 023019 (2021).
  22. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L042007 for (1) measurement setup for general optical modes; (2) details of the experimental setup including calibration; (3) security analysis against coherent attack and an example of strongly correlated noise model.
  23. S. Etcheverry, G. Cañas, E. S. Gómez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, Quantum key distribution session with 16-dimensional photonic states, Sci. Rep. 3, 2316 (2013).
  24. M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O'Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, High-dimensional quantum cryptography with twisted light, New J. Phys. 17, 033033 (2015).
  25. A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, and E. Karimi, High-dimensional intracity quantum cryptography with structured photons, Optica 4, 1006 (2017).
  26. N. T. Islam, C. Cahall, A. Aragoneses, A. Lezama, J. Kim, and D. J. Gauthier, Robust and Stable Delay Interferometers with Application to d-Dimensional Time-Frequency Quantum Key Distribution, Phys. Rev. Appl. 7, 044010 (2017).
  27. N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, Provably secure and high-rate quantum key distribution with time-bin qudits, Sci. Adv. 3, e1701491 (2017).
  28. Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits, npj Quantum Inf. 3, 25 (2017).
  29. G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers, Phys. Rev. A 96, 022317 (2017).
  30. I. Vagniluca, B. Da Lio, D. Rusca, D. Cozzolino, Y. Ding, H. Zbinden, A. Zavatta, L. K. Oxenløwe, and D. Bacco, Efficient Time-Bin Encoding for Practical High-Dimensional Quantum Key Distribution, Phys. Rev. Appl. 14, 014051 (2020).
  31. X.-M. Hu, C. Zhang, Y. Guo, F.-X. Wang, W.-B. Xing, C.-X. Huang, B.-H. Liu, Y.-F. Huang, C.-F. Li, G.-C. Guo, X. Gao, M. Pivoluska, and M. Huber, Pathways for Entanglement-Based Quantum Communication in the Face of High Noise, Phys. Rev. Lett. 127, 110505 (2021).
  32. Q.-K. Wang, F.-X. Wang, J. Liu, W. Chen, Z.-F. Han, A. Forbes, and J. Wang, High-Dimensional Quantum Cryptography with Hybrid Orbital-Angular-Momentum States through 25 km of Ring-Core Fiber: A Proof-of-Concept Demonstration, Phys. Rev. Appl. 15, 064034 (2021).
  33. T. Inagaki, N. Matsuda, O. Tadanaga, M. Asobe, and H. Takesue, Entanglement distribution over 300 km of fiber, Opt. Express 21, 23241 (2013).
  34. T. Ikuta and H. Takesue, Four-dimensional entanglement distribution over 100 km, Sci. Rep. 8, 817 (2018).
  35. M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases, Phys. Rev. A 88, 032305 (2013).
  36. N. T. Islam, Charles Ci Wen Lim, C. Cahall, J. Kim, and D. J. Gauthier, Securing quantum key distribution systems using fewer states, Phys. Rev. A 97, 042347 (2018).
  37. N. T. Islam, C. C. W. Lim, C. Cahall, B. Qi, J. Kim, and D. J. Gauthier, Scalable high-rate, high-dimensional time-bin encoding quantum key distribution, Quantum Sci. Technol. 4, 035008 (2019).
  38. F. Bussieres, Y. Soudagar, G. Berlin, S. Lacroix, and N. Godbout, Deterministic unitary operations on time-bin qudits for quantum communication, arXiv:quant-ph/0608183.
  39. H. Takesue and Y. Noguchi, Implementation of quantum state tomography for time-bin entangled photon pairs, Opt. Express 17, 10976 (2009).
  40. T. M. Rambo, Low-loss, all-optical, quantum switching for interferometric processing of weak signals, Ph.D. thesis, Northwestern University, 2016.
  41. T. Honjo, K. Inoue, and H. Takahashi, Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer, Opt. Lett. 29, 2797 (2004).
  42. H. Takesue and K. Inoue, Generation of 1.5-μm band time-bin entanglement using spontaneous fiber four-wave mixing and planar light-wave circuit interferometers, Phys. Rev. A 72, 041804(R) (2005).
  43. H.-P. Lo, T. Ikuta, N. Matsuda, T. Honjo, and H. Takesue, Entanglement generation using a controlled-phase gate for time-bin qubits, Appl. Phys. Express 11, 092801 (2018).
  44. H.-P. Lo, T. Ikuta, N. Matsuda, T. Honjo, W. J. Munro, and H. Takesue, Quantum Process Tomography of a Controlled-Phase Gate for Time-Bin Qubits, Phys. Rev. Appl. 13, 034013 (2020).
  45. R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, Bell-Type Test of Energy-Time Entangled Qutrits, Phys. Rev. Lett. 93, 010503 (2004).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation