Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons

Frédéric Bouchard1, Khabat Heshami2, Duncan England2, Robert Fickler1, Robert W. Boyd1,3,4, Berthold-Georg Englert5,6,7, Luis L. Sánchez-Soto3,8, and Ebrahim Karimi1,3,9

1Department of physics, University of Ottawa, Advanced Research Complex, 25 Templeton, Ottawa ON Canada, K1N 6N5
2National Research Council of Canada, 100 Sussex Drive, Ottawa ON Canada, K1A 0R6
3Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, 91058 Erlangen, Germany
4Institute of Optics, University of Rochester, Rochester, NY 14627, USA
5Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
6Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore.
7MajuLab, CNRS-UNS-NUS-NTU International Joint Unit, UMI 3654, Singapore.
8Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
9Department of Physics, Institute for Advanced Studies in Basic Sciences, 45137-66731 Zanjan, Iran.

Quantum key distribution is on the verge of real world applications, where perfectly secure information can be distributed among multiple parties. Several quantum cryptographic protocols have been theoretically proposed and independently realized in different experimental conditions. Here, we develop an experimental platform based on high-dimensional orbital angular momentum states of single photons that enables implementation of multiple quantum key distribution protocols with a single experimental apparatus. Our versatile approach allows us to experimentally survey different classes of quantum key distribution techniques, such as the 1984 Bennett & Brassard (BB84), tomographic protocols including the six-state and the Singapore protocol, and to investigate, for the first time, a recently introduced differential phase shift (Chau15) protocol using twisted photons. This enables us to experimentally compare the performance of these techniques and discuss their benefits and deficiencies in terms of noise tolerance in different dimensions.

► BibTeX data

► References

[1] Gisin, N., Ribordy, G., Tittel, W. & Zbinden, H., Quantum cryptography, Rev. Mod. Phys. 74, 145 (2002).

[2] Bennett, C. H. & Brassard, G., Quantum cryptography: Public key distribution and coin tossing, Proceedings of the ieee international conference on computers, systems, and signal processing, bangalore, india, 1984 (1984).

[3] Scarani, V. et al., The security of practical quantum key distribution, Rev. Mod. Phys. 81, 1301 (2009).

[4] Wiesner, S. Conjugate coding, ACM Sigact News 15, 78-88 (1983).

[5] Hillery, M., Bužek, V. & Berthiaume, A. Quantum secret sharing, Phys. Rev. A 59, 1829 (1999).

[6] Scarani, V., Iblisdir, S., Gisin, N. & Acin, A. Quantum cloning, Rev. Mod. Phys. 77, 1225 (2005).

[7] Simon, C. et al. Quantum memories, Eur. Phys. J. D 58, 1-22 (2010).

[8] Werner, M. & Milburn, G. Eavesdropping using quantum-nondemolition measurements, Phys. Rev. A 47, 639 (1993).

[9] Bennett, C. H., Brassard, G., Crépeau, C. & Maurer, U. M. Generalized privacy amplification, IEEE T. Inform. Theory 41, 1915-1923 (1995).

[10] Bechmann-Pasquinucci, H. & Tittel, W. Quantum cryptography using larger alphabets, Phys. Rev. A 61, 062308 (2000).

[11] Cerf, N. J., Bourennane, M., Karlsson, A. & Gisin, N. Security of quantum key distribution using d-level systems, Phys. Rev. Lett. 88, 127902 (2002).

[12] Allen, L., Beijersbergen, M. W., Spreeuw, R. & Woerdman, J. Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes, Phys. Rev. A 45, 8185 (1992).

[13] Heckenberg, N., McDuff, R., Smith, C. & White, A. Generation of optical phase singularities by computer-generated holograms, Opt. Lett. 17, 221-223 (1992).

[14] Bolduc, E., Bent, N., Santamato, E., Karimi, E. & Boyd, R. W. Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram, Opt. Lett. 38, 3546-3549 (2013).

[15] Forbes, A., Dudley, A. & McLaren, M. Creation and detection of optical modes with spatial light modulators, Advances in Optics and Photonics 8, 200-227 (2016).

[16] Gröblacher, S., Jennewein, T., Vaziri, A., Weihs, G. & Zeilinger, A. Experimental quantum cryptography with qutrits, New J. Phys. 8, 75 (2006).

[17] Mafu, M. et al. Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases, Phys. Rev. A 88, 032305 (2013).

[18] Mirhosseini, M. et al. High-dimensional quantum cryptography with twisted light, New J. Phys. 17, 033033 (2015).

[19] D'ambrosio, V. et al. Complete experimental toolbox for alignment-free quantum communication, Nat. Commun. 3, 961 (2012).

[20] Vallone, G. et al. Free-space quantum key distribution by rotation-invariant twisted photons, Phys. Rev. Lett. 113, 060503 (2014).

[21] Krenn, M., Handsteiner, J., Fink, M., Fickler, R. & Zeilinger, A. Twisted photon entanglement through turbulent air across Vienna, PNAS 112, 14197-14201 (2015).

[22] Sit, A. et al. High-dimensional intracity quantum cryptography with structured photons, Optica 4, 1006-1010 (2017).

[23] Cardano, F. et al. Quantum walks and wavepacket dynamics on a lattice with twisted photons, Science Adv. 1, e1500087 (2015).

[24] Cardano, F. et al. Statistical moments of quantum-walk dynamics reveal topological quantum transitions, Nat. Commun. 7, 11439 (2016).

[25] Cardano, F. et al. Detection of zak phases and topological invariants in a chiral quantum walk of twisted photons, Nature Commun. 8, 15516 (2017).

[26] Babazadeh, A. et al. High-dimensional single-photon quantum gates: concepts and experiments, Phys. Rev. Lett. 119, 180510 (2017).

[27] Erhard, M., Fickler, R., Krenn, M. & Zeilinger, A. Twisted photons: New quantum perspectives in high dimensions, Light Sci. Appl. (2018).

[28] Bruß, D. Optimal eavesdropping in quantum cryptography with six states, Phys. Rev. Lett. 81, 3018 (1998).

[29] Liang, Y. C., Kaszlikowski, D., Englert, B.-G., Kwek, L. C. & Oh, C. H. Tomographic quantum cryptography, Phys. Rev. A 68, 022324 (2003).

[30] Englert, B.-G. et al. Efficient and robust quantum key distribution with minimal state tomography, arXiv preprint quant-ph/​0412075 (2008).

[31] Durt, T., Englert, B.-G., Bengtsson, I. & Życzkowski, K. On mutually unbiased bases, Int. J. Quantum Inf. 8, 535-640 (2010).

[32] Renes, J. M., Blume-Kohout, R., Scott, A. J. & Caves, C. M. Symmetric informationally complete quantum measurements, J. Math. Phys. 45, 2171-2180 (2004).

[33] Chuang, I. L. & Nielsen, M. A. Prescription for experimental determination of the dynamics of a quantum black box, J. Mod. Opt. 44, 2455-2467 (1997).

[34] Lo, H.-K., Chau, H. F., & Ardehali, M. Efficient Quantum Key Distribution Scheme and a Proof of Its Unconditional Security, Journal of Cryptology 18, 133-165 (2005).

[35] Brádler, K., Mirhosseini, M., Fickler, R., Broadbent, A. & Boyd, R. Finite-key security analysis for multilevel quantum key distribution, New Journal of Physics 18, 073030 (2016).

[36] Ding, Y. et al. High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits, npj Quantum Information 3, 25 (2017).

[37] Genovese, M. & Traina, P. Review on qudits production and their application to quantum communication and studies on local realism, Advanced Science Letters 1, 153-160 (2008).

[38] Bouchard, F., Fickler, R., Boyd, R. W. & Karimi, E. High-dimensional quantum cloning and applications to quantum hacking, Science Adv. 3, e1601915 (2017).

[39] Sheridan, L. & Scarani, V. Security proof for quantum key distribution using qudit systems, Phys. Rev. A 82, 030301 (2010).

[40] D'ambrosio, V. et al. Test of mutually unbiased bases for six-dimensional photonic quantum systems, Sci. Rep. 3, 2726 (2013).

[41] Ekert, A. K. Quantum cryptography based on bell's theorem, Phys. Rev. Lett. 67, 661 (1991).

[42] Bent, N. et al. Experimental realization of quantum tomography of photonic qudits via symmetric informationally complete positive operator-valued measures, Phys. Rev. X 5, 041006 (2015).

[43] Inoue, K., Waks, E. & Yamamoto, Y. Differential phase shift quantum key distribution, Phys. Rev. Lett. 89, 037902 (2002).

[44] Sasaki, T., Yamamoto, Y. & Koashi, M. Practical quantum key distribution protocol without monitoring signal disturbance, Nature 509, 475 (2014).

[45] Bouchard F., Sit A., Heshami K., Fickler R. & Karimi E. Round-robin differential phase-shift quantum key distribution with twisted photons, Phys. Rev. A 98, 010301(R) (2018).

[46] Chau, H. Quantum key distribution using qudits that each encode one bit of raw key, Phys. Rev. A 92, 062324 (2015).

[47] Chau, H., Wang, Q. & Wong, C. Experimentally feasible quantum-key-distribution scheme using qubit-like qudits and its comparison with existing qubit-and qudit-based protocols, Phys. Rev. A 95, 022311 (2017).

[48] Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons, Nature 412, 313-316 (2001).

[49] Qassim, H. et al. Limitations to the determination of a laguerre-gauss spectrum via projective, phase-flattening measurement, J. Opt. Soc. Am. B 31, A20-A23 (2014).

[50] Waks, E. et al. Security aspects of quantum key distribution with sub-Poisson light, Phys. Rev. A 66, 042315 (2002).

[51] Schiavon, M. et al. Heralded single-photon sources for quantum-key-distribution applications, Phys. Rev. A 93, 012331 (2016).

[52] Wang, S. et al. Proof-of-principle experimental realization of a qubit-like qudit-based quantum key distribution scheme, Quantum Sci. Technol. 3, 025006 (2018).

[53] Bouchard, F., Sit, A., Hufnagel, F., Abbas, A., Zhang, Y., Heshami, K., Fickler, R., Marquardt, C., Leuchs, G., Boyd, R. W. & Karimi, E. Quantum cryptography with twisted photons through an outdoor underwater channel, Opt. Express 26, 22563-22573 (2018).

[54] Scott, A. J. & Grassl, M. Symmetric informationally complete positive-operator-valued measures: A new computer study, J. Math. Phys. 51, 042203 (2010).

[55] Ndagano, B. et al. Characterizing quantum channels with non-separable states of classical light, Nat. Phys. 13, 397 (2017).

[56] Bongioanni, I., Sansoni, L., Sciarrino, F., Vallone, G., & Mataloni, P., Experimental quantum process tomography of non-trace-preserving maps, Phys. Rev. A 82, 042307 (2010).

[57] Bouchard, F., Hufnagel, F., Koutnỳ, D., Abbas, A., Sit, A., Heshami, K., Fickler, R. & Karimi, E., Full characterization of a high-dimensional quantum communication channel, arXiv preprint arXiv:1806.08018 (2018).

[58] Tomamichel, M. et al. Tight finite-key analysis for quantum cryptography, Nat. Commun. 3, 634 (2012).

Cited by

[1] Fang-Xiang Wang, Wei Chen, Zhen-Qiang Yin, Shuang Wang, Guang-Can Guo, and Zheng-Fu Han, "Characterizing High-Quality High-Dimensional Quantum Key Distribution by State Mapping Between Different Degrees of Freedom", Physical Review Applied 11 2, 024070 (2019).

[2] Dongkai Zhang, Xiaodong Qiu, Wuhong Zhang, and Lixiang Chen, "Violation of a Bell inequality in two-dimensional state spaces for radial quantum number", Physical Review A 98 4, 042134 (2018).

[3] J. Miguel-Ramiro and W. Dür, "Efficient entanglement purification protocols for d -level systems", Physical Review A 98 4, 042309 (2018).

[4] Yonggi Jo, Hee Park, Seung-Woo Lee, and Wonmin Son, "Efficient High-Dimensional Quantum Key Distribution with Hybrid Encoding", Entropy 21 1, 80 (2019).

[5] Frédéric Bouchard, Alicia Sit, Khabat Heshami, Robert Fickler, and Ebrahim Karimi, "Round-robin differential-phase-shift quantum key distribution with twisted photons", Physical Review A 98 1, 010301 (2018).

[6] Hugo Defienne, Matthew Reichert, and Jason W. Fleischer, "Adaptive Quantum Optics with Spatially Entangled Photon Pairs", Physical Review Letters 121 23, 233601 (2018).

[7] Sebastian Ecker, Frédéric Bouchard, Lukas Bulla, Florian Brandt, Oskar Kohout, Fabian Steinlechner, Robert Fickler, Mehul Malik, Yelena Guryanova, Rupert Ursin, and Marcus Huber, "Entanglement distribution beyond qubits or: How I stopped worrying and learned to love the noise", arXiv:1904.01552 (2019).

[8] Armin Tavakoli, Denis Rosset, and Marc-Olivier Renou, "Enabling Computation of Correlation Bounds for Finite-Dimensional Quantum Systems via Symmetrization", Physical Review Letters 122 7, 070501 (2019).

[9] Wei Li and Shengmei Zhao, "Generation of two-photon orbital-angular-momentum entanglement with a high degree of entanglement", Applied Physics Letters 114 4, 041105 (2019).

[10] Frédéric Bouchard, Felix Hufnagel, Dominik Koutný, Aazad Abbas, Alicia Sit, Khabat Heshami, Robert Fickler, and Ebrahim Karimi, "Quantum process tomography of a high-dimensional quantum communication channel", Quantum 3, 138 (2019).

The above citations are from Crossref's cited-by service (last updated 2019-05-20 22:39:45) and SAO/NASA ADS (last updated 2019-05-20 22:39:46). The list may be incomplete as not all publishers provide suitable and complete citation data.