Abstract
Owing to physical orientations and birefringence effects, practical quantum information protocols utilizing optical polarization need to handle misalignment between preparation and measurement reference frames. For any such capable system, an important question is how many resources – for example, measured single photons – are needed to reliably achieve alignment precision sufficient for the desired quantum protocol. Here, we study the performance of a polarization-frame alignment scheme used in prior laboratory and field quantum key distribution (QKD) experiments by performing Monte Carlo numerical simulations. The scheme utilizes, to the extent possible, the same single-photon-level signals and measurements as for the QKD protocol being supported. Even with detector noise and imperfect sources, our analysis shows that only a small fraction of resources from the overall signal – a few hundred photon detections, in total – are required for good performance, restoring the state to better than 99% of its original quality.
Funding source: NSERC
Funding source: Canadian Space Agency
Funding source: CFI
Funding source: CIFAR
Funding source: Industry Canada
Funding source: FedDev Ontario
Funding source: Ontario Research Fund
Acknowledgments
The authors thank Nikolay Gigov for helpful discussions.
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: This work was supported by the NSERC, Canadian Space Agency, CFI, CIFAR, Industry Canada, FedDev Ontario, and Ontario Research Fund (Canada). B.L.H. acknowledges support from NSERC Banting Postdoctoral Fellowships (Canada).
Competing interests: The authors declare no conflicts of interest regarding this article.
References
[1] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys., vol. 74, pp. 145–195, 2002. https://doi.org/10.1103/revmodphys.74.145.Search in Google Scholar
[2] V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys., vol. 81, pp. 1301–1350, 2009. https://doi.org/10.1103/revmodphys.81.1301.Search in Google Scholar
[3] C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India, 1984, pp. 175–179.Search in Google Scholar
[4] E. R. Jeffrey, J. B. Altepeter, M. Colci, and P. G. Kwiat, “Optical implementation of quantum orienteering,” Phys. Rev. Lett., vol. 96, p. 150503, 2006. https://doi.org/10.1103/physrevlett.96.150503.Search in Google Scholar
[5] Canadian Space Agency, Quantum encryption and science satellite (QEYSSat). Available at: https://asc-csa.gc.ca/eng/sciences/qeyssat.asp [accessed: Apr. 21, 2020].Search in Google Scholar
[6] J.-P. Bourgoin, N. Gigov, B. L. Higgins, et al., “Experimental quantum key distribution with simulated ground-to-satellite photon losses and processing limitations,” Phys. Rev. A, vol. 92, p. 052339, 2015. https://doi.org/10.1103/physreva.92.052339.Search in Google Scholar
[7] J.-P. Bourgoin, B. L. Higgins, N. Gigov, et al., “Free-space quantum key distribution to a moving receiver,” Opt. Express, vol. 23, p. 33437, 2015. https://doi.org/10.1364/oe.23.033437.Search in Google Scholar
[8] C. J. Pugh, S. Kaiser, J.-P. Bourgoin, et al., “Airborne demonstration of a quantum key distribution receiver payload,” Quantum Sci. Technol., vol. 2, p. 024009, 2017. https://doi.org/10.1088/2058-9565/aa701f.Search in Google Scholar
[9] E. Bagan, M. Baig, A. Brey, R. Muñoz-Tapia, and R. Tarrach, “Optimal strategies for sending information through a quantum channel,” Phys. Rev. Lett., vol. 85, pp. 5230–5233, 2000. https://doi.org/10.1103/physrevlett.85.5230.Search in Google Scholar
[10] A. Peres and P. F. Scudo, “Entangled quantum states as direction indicators,” Phys. Rev. Lett., vol. 86, pp. 4160–4162, 2001. https://doi.org/10.1103/physrevlett.86.4160.Search in Google Scholar
[11] E. Bagan, M. Baig, and R. Muñoz-Tapia, “Communication of spin directions with product states and finite measurements,” Phys. Rev. A, vol. 64, p. 022305, 2001. https://doi.org/10.1103/physreva.64.022305.Search in Google Scholar
[12] E. Bagan, M. Baig, and R. Muñoz-Tapia, “Aligning reference frames with quantum states,” Phys. Rev. Lett., vol. 87, p. 257903, 2001. https://doi.org/10.1103/physrevlett.87.257903.Search in Google Scholar
[13] E. Bagan, M. Baig, and R. Muñoz-Tapia, “Quantum reverse engineering and reference-frame alignment without nonlocal correlations,” Phys. Rev. A, vol. 70, p. 030301, 2004. https://doi.org/10.1103/physreva.70.030301.Search in Google Scholar
[14] M. A. Ballester, “Estimation of unitary quantum operations,” Phys. Rev. A, vol. 69, p. 022303, 2004. https://doi.org/10.1103/physreva.69.022303.Search in Google Scholar
[15] A. Laing, V. Scarani, J. G. Rarity, and J. L. O’Brien, “Reference-frame-independent quantum key distribution,” Phys. Rev. A, vol. 82, p. 012304, 2010. https://doi.org/10.1103/physreva.82.012304.Search in Google Scholar
[16] V. D’Ambrosio, E. Nagali, S. P. Walborn, et al., “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun., vol. 3, p. 961, 2012. https://doi.org/10.1038/ncomms1951.Search in Google Scholar
[17] J. Wabnig, D. Bitauld, H. W. Li, A. Laing, J. L. O’Brien, A. O. Niskanen, “Demonstration of free-space reference frame independent quantum key distribution,” New J. Phys., vol. 15, p. 073001, 2013. https://doi.org/10.1088/1367-2630/15/7/073001.Search in Google Scholar
[18] L. Wen-Ye, W. Hao, Y. Zhen-Qiang, et al., “Tomographic approach in three-orthogonal-basis quantum key distribution,” Commun. Theor. Phys., vol. 64, p. 295, 2015. https://doi.org/10.1088/0253-6102/64/3/295.Search in Google Scholar
[19] G. B. Xavier, G. Vilela de Faria, T. Ferreira da Silva, G. P. Temporão, and J. P. von der Weid, “Active polarization control for quantum communication in long-distance optical fibers with shared telecom traffic,” Micro. Opt. Tech. Lett., vol. 53, pp. 2661–2665, 2011. https://doi.org/10.1002/mop.26320.Search in Google Scholar
[20] M. Sasaki, M. Fujiwara, H. Ishizuka, et al., “Field test of quantum key distribution in the Tokyo QKD network,” Opt. Express, vol. 19, pp. 10387–10409, 2011. https://doi.org/10.1364/OE.19.010387.Search in Google Scholar
[21] J. Jin, J.-P. Bourgoin, R. Tannous, et al., “Genuine time-bin-encoded quantum key distribution over a turbulent depolarizing free-space channel,” Opt. Express, vol. 27, pp. 37214–37223, 2019. https://doi.org/10.1364/oe.27.037214.Search in Google Scholar
[22] W. K. Wootters and B. D. Fields, “A Wigner-function formulation of finite-state quantum mechanics,” Ann. Phys., vol. 191, pp. 363–381, 1989. https://doi.org/10.1016/0003-4916(89)90322-9.Search in Google Scholar
[23] Z. Hradil, J. Summhammer, G. Badurek, and H. Rauch, “Reconstruction of the spin state,” Phys. Rev. A, vol. 62, p. 014101, 2000. https://doi.org/10.1103/physreva.62.014101.Search in Google Scholar
[24] J.-P. Bourgoin, E. Meyer-Scott, B. L. Higgins, et al., “A comprehensive design and performance analysis of low Earth orbit satellite quantum communication,” New J. Phys., vol. 15, p. 023006, 2013. https://doi.org/10.1088/1367-2630/15/2/023006.Search in Google Scholar
[25] J. Řeháček, B.-G. Englert, and D. Kaszlikoski, “Minimal qubit tomography,” Phys. Rev. A, vol. 70, p. 052321, 2004. https://doi.org/10.1103/physreva.70.052321.Search in Google Scholar
[26] S. Massar and S. Popescu, “Optimal extraction of information from finite quantum ensembles,” Phys. Rev. Lett., vol. 74, pp. 1259–1263, 1995. https://doi.org/10.1103/physrevlett.74.1259.Search in Google Scholar
[27] S. T. Flammia and Y.-K. Liu, “Direct fidelity estimation from few pauli measurements,” Phys. Rev. Lett., vol. 106, p. 230501, 2011. https://doi.org/10.1103/physrevlett.106.230501.Search in Google Scholar
[28] A. Ling, K. P. Soh, A. Lamas-Linares, and C. Kurtsiefer, “An optimal photon counting polarimeter,” J. Mod. Opt., vol. 53, pp. 1523–1528, 2006. https://doi.org/10.1080/09500340600674242.Search in Google Scholar
[29] S. G. Roy, O. M. Awartani, P. Sen, B. T. O’Connor, and M. W. Kudenov, “Intrinsic coincident linear polarimetry using stacked organic photovoltaics,” Opt. Express, vol. 24, pp. 14737–14747, 2016. https://doi.org/10.1364/oe.24.014737.Search in Google Scholar
[30] P. Kolenderski and R. Demkowicz-Dobrzanski, “Optimal state for keeping reference frames aligned and the platonic solids,” Phys. Rev. A, vol. 78, p. 052333, 2008. https://doi.org/10.1103/physreva.78.052333.Search in Google Scholar
[31] J. Fisher, A. Kodanev, and M. Nazarathy, “Multi-degree-of-freedom stabilization of large-scale photonic-integrated circuits,” J. Lightwave Technol., vol. 33, pp. 2146–2166, 2015. https://doi.org/10.1109/jlt.2015.2391194.Search in Google Scholar
[32] Y.-Y. Ding, W. Chen, H. Chen, et al., “Polarization-basis tracking scheme for quantum key distribution using revealed sifted key bits,” Opt. Lett., vol. 42, pp. 1023–1026, 2017. https://doi.org/10.1364/ol.42.001023.Search in Google Scholar
© 2020 Brendon L. Higgins et al.,published by De Gruyter
