Device-independent quantum key distribution with single-photon sources

Jan Kołodyński1,2, Alejandro Máttar2, Paul Skrzypczyk3, Erik Woodhead2,4, Daniel Cavalcanti2, Konrad Banaszek1,5, and Antonio Acín2,6

1Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
2ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
3H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
4Laboratoire d'Information Quantique, Université libre de Bruxelles (ULB), 1050 Bruxelles, Belgium
5Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland
6ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


$\textit{Device-independent quantum key distribution}$ protocols allow two honest users to establish a secret key with minimal levels of trust on the provider, as security is proven without any assumption on the inner working of the devices used for the distribution. Unfortunately, the implementation of these protocols is challenging, as it requires the observation of a large Bell-inequality violation between the two distant users. Here, we introduce novel photonic protocols for device-independent quantum key distribution exploiting $\textit{single-photon sources}$ and $\textit{heralding-type architectures}$. The heralding process is designed so that transmission losses become irrelevant for security. We then show how the use of single-photon sources for entanglement distribution in these architectures, instead of standard entangled-pair generation schemes, provides significant improvements on the attainable key rates and distances over previous proposals. Given the current progress in single-photon sources, our work opens up a promising avenue for device-independent quantum key distribution implementations.

► BibTeX data

► References

[1] D. Mayers and A. Yao. Quantum cryptography with imperfect apparatus. In Proceedings of the 39th IEEE Conference on Foundations of Computer Science, 1998.

[2] Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, and Valerio Scarani. Device-Independent Security of Quantum Cryptography against Collective Attacks. Phys. Rev. Lett., 98: 230501, June 2007. 10.1103/​PhysRevLett.98.230501.

[3] Stefano Pironio, Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, and Valerio Scarani. Device-independent quantum key distribution secure against collective attacks. New J. Phys., 11 (4): 045021, April 2009. 10.1088/​1367-2630/​11/​4/​045021.

[4] Lluis Masanes, Stefano Pironio, and Antonio Acin. Secure device-independent quantum key distribution with causally independent measurement devices. Nat. Commun., 2: 238–, March 2011. 10.1038/​ncomms1244.

[5] S. Pironio, Ll. Masanes, A. Leverrier, and A. Acín. Security of Device-Independent Quantum Key Distribution in the Bounded-Quantum-Storage Model. Phys. Rev. X, 3: 031007, August 2013. 10.1103/​PhysRevX.3.031007.

[6] Umesh Vazirani and Thomas Vidick. Fully device-independent quantum key distribution. Phys. Rev. Lett., 113: 140501, September 2014. 10.1103/​PhysRevLett.113.140501.

[7] R. Arnon-Friedman, R. Renner, and T. Vidick. Simple and tight device-independent security proofs. SIAM J. Comput., 48 (1): 181–225, 2019. 10.1137/​18M1174726.

[8] John Bell. On the Einstein-Podolsky-Rosen Paradox. Physics, 1: 195–200, 1964. 10.1103/​physicsphysiquefizika.1.195.

[9] Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. Bell nonlocality. Rev. Mod. Phys., 86: 419–478, April 2014. 10.1103/​RevModPhys.86.419.

[10] Philip M. Pearle. Hidden-variable example based upon data rejection. Phys. Rev. D, 2: 1418–1425, October 1970. 10.1103/​PhysRevD.2.1418.

[11] Ilja Gerhardt, Qin Liu, Antía Lamas-Linares, Johannes Skaar, Valerio Scarani, Vadim Makarov, and Christian Kurtsiefer. Experimentally Faking the Violation of Bell's Inequalities. Phys. Rev. Lett., 107: 170404, October 2011. 10.1103/​PhysRevLett.107.170404.

[12] John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 23: 880–884, October 1969. 10.1103/​PhysRevLett.23.880.

[13] Philippe H. Eberhard. Background level and counter efficiencies required for a loophole-free Einstein-Podolsky-Rosen experiment. Phys. Rev. A, 47: R747–R750, February 1993. 10.1103/​PhysRevA.47.R747.

[14] M. A. Rowe, D. Kielpinski, V. Meyer, W. M.. Itano, C. Monroe, and D. J. Wineland. Experimental violation of a Bell's inequality with efficient detection. Nature, 409, February 2001. 10.1038/​35057215.

[15] D. N. Matsukevich, P. Maunz, D. L. Moehring, S. Olmschenk, and C. Monroe. Bell inequality violation with two remote atomic qubits. Phys. Rev. Lett., 100: 150404, April 2008. 10.1103/​PhysRevLett.100.150404.

[16] Julian Hofmann, Michael Krug, Norbert Ortegel, Lea Gérard, Markus Weber, Wenjamin Rosenfeld, and Harald Weinfurter. Heralded entanglement between widely separated atoms. Science, 337 (6090): 72–75, 2012. 10.1126/​science.1221856.

[17] B. Hensen, H. Bernien, A. E. Dreau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellan, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526: 682–686, October 2015. 10.1038/​nature15759.

[18] Alejandro Máttar, Jonatan Bohr Brask, and Antonio Acín. Device-independent quantum key distribution with spin-coupled cavities. Phys. Rev. A, 88: 062319, December 2013. 10.1103/​PhysRevA.88.062319.

[19] Nicolas Brunner, Andrew B Young, Chengyong Hu, and John G Rarity. Proposal for a loophole-free Bell test based on spin–photon interactions in cavities. New J. Phys., 15 (10): 105006, 2013. 10.1088/​1367-2630/​15/​10/​105006.

[20] N. Sangouard, J.-D. Bancal, N. Gisin, W. Rosenfeld, P. Sekatski, M. Weber, and H. Weinfurter. Loophole-free Bell test with one atom and less than one photon on average. Phys. Rev. A, 84: 052122, November 2011. 10.1103/​PhysRevA.84.052122.

[21] Marissa Giustina, Alexandra Mech, Sven Ramelow, Bernhard Wittmann, Johannes Kofler, Jorn Beyer, Adriana Lita, Brice Calkins, Thomas Gerrits, Sae Woo Nam, Rupert Ursin, and Anton Zeilinger. Bell violation using entangled photons without the fair-sampling assumption. Nature, 497: 227–230, September 2013. 10.1038/​nature12012.

[22] B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat. Detection-loophole-free test of quantum nonlocality, and applications. Phys. Rev. Lett., 111: 130406, September 2013. 10.1103/​PhysRevLett.111.130406.

[23] Marissa Giustina, Marijn A. M. Versteegh, Sören Wengerowsky, Johannes Handsteiner, Armin Hochrainer, Kevin Phelan, Fabian Steinlechner, Johannes Kofler, Jan-Åke Larsson, Carlos Abellán, Waldimar Amaya, Valerio Pruneri, Morgan W. Mitchell, Jörn Beyer, Thomas Gerrits, Adriana E. Lita, Lynden K. Shalm, Sae Woo Nam, Thomas Scheidl, Rupert Ursin, Bernhard Wittmann, and Anton Zeilinger. Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons. Phys. Rev. Lett., 115: 250401, December 2015. 10.1103/​PhysRevLett.115.250401.

[24] Lynden K. Shalm, Evan Meyer-Scott, Bradley G. Christensen, Peter Bierhorst, Michael A. Wayne, Martin J. Stevens, Thomas Gerrits, Scott Glancy, Deny R. Hamel, Michael S. Allman, Kevin J. Coakley, Shellee D. Dyer, Carson Hodge, Adriana E. Lita, Varun B. Verma, Camilla Lambrocco, Edward Tortorici, Alan L. Migdall, Yanbao Zhang, Daniel R. Kumor, William H. Farr, Francesco Marsili, Matthew D. Shaw, Jeffrey A. Stern, Carlos Abellán, Waldimar Amaya, Valerio Pruneri, Thomas Jennewein, Morgan W. Mitchell, Paul G. Kwiat, Joshua C. Bienfang, Richard P. Mirin, Emanuel Knill, and Sae Woo Nam. Strong Loophole-Free Test of Local Realism. Phys. Rev. Lett., 115: 250402, December 2015. 10.1103/​PhysRevLett.115.250402.

[25] Igor Aharonovich, Dirk Englund, and Milos Toth. Solid-state single-photon emitters. Nat. Photonics, 10 (10): 631–641, October 2016. ISSN 1749-4885. 10.1038/​nphoton.2016.186.

[26] Markus Müller, Samir Bounouar, Klaus D Jöns, M Glässl, and P Michler. On-demand generation of indistinguishable polarization-entangled photon pairs. Nat. Photonics, 8 (3): 224–228, March 2014. ISSN 1749-4885. 10.1038/​nphoton.2013.377.

[27] Julien Claudon, Joel Bleuse, Nitin Singh Malik, Maela Bazin, Perine Jaffrennou, Niels Gregersen, Christophe Sauvan, Philippe Lalanne, and Jean-Michel Gerard. A highly efficient single-photon source based on a quantum dot in a photonic nanowire. Nat. Photonics, 4 (3): 174–177, March 2010. ISSN 1749-4885. 10.1038/​nphoton.2009.287.

[28] Juan C Loredo, Nor A Zakaria, Niccolo Somaschi, Carlos Anton, Lorenzo De Santis, Valerian Giesz, Thomas Grange, Matthew A Broome, Olivier Gazzano, Guillaume Coppola, et al. Scalable performance in solid-state single-photon sources. Optica, 3 (4): 433–440, 2016. 10.1364/​OPTICA.3.000433.

[29] Hui Wang, Z.-C. Duan, Y.-H. Li, Si Chen, J.-P. Li, Y.-M. He, M.-C. Chen, Yu He, X. Ding, Cheng-Zhi Peng, Christian Schneider, Martin Kamp, Sven Höfling, Chao-Yang Lu, and Jian-Wei Pan. Near-transform-limited single photons from an efficient solid-state quantum emitter. Phys. Rev. Lett., 116: 213601, May 2016. 10.1103/​PhysRevLett.116.213601.

[30] Je-Hyung Kim, Tao Cai, Christopher J. K. Richardson, Richard P. Leavitt, and Edo Waks. Two-photon interference from a bright single-photon source at telecom wavelengths. Optica, 3 (6): 577–584, June 2016. 10.1364/​OPTICA.3.000577.

[31] N. Somaschi, V. Giesz, L. De Santis, J. C. Loredo, M. P. Almeida, G. Hornecker, S. L. Portalupi, T. Grange, C. Anton, J. Demory, C. Gomez, I. Sagnes, N. D. Lanzillotti-Kimura, A. Lemaitre, A. Auffeves, A. G. White, L. Lanco, and P. Senellart. Near-optimal single-photon sources in the solid state. Nat. Photonics, March 2016. 10.1038/​nphoton.2016.23.

[32] Xing Ding, Yu He, Z.-C. Duan, Niels Gregersen, M.-C. Chen, S. Unsleber, S. Maier, Christian Schneider, Martin Kamp, Sven Höfling, Chao-Yang Lu, and Jian-Wei Pan. On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar. Phys. Rev. Lett., 116: 020401, January 2016. 10.1103/​PhysRevLett.116.020401.

[33] Paul G. Kwiat, Klaus Mattle, Harald Weinfurter, Anton Zeilinger, Alexander V. Sergienko, and Yanhua Shih. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett., 75: 4337–4341, December 1995. 10.1103/​PhysRevLett.75.4337.

[34] Claude E Shannon. Communication theory of secrecy systems. Bell Labs Tech. J., 28 (4): 656–715, 1949. 10.1002/​j.1538-7305.1949.tb00928.x.

[35] Alejandro Máttar and Antonio Acín. Implementations for device-independent quantum key distribution. Phys. Scr., 91 (4): 043003, 2016. 10.1088/​0031-8949/​91/​4/​043003.

[36] Nicolas Gisin, Stefano Pironio, and Nicolas Sangouard. Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier. Phys. Rev. Lett., 105: 070501, August 2010. 10.1103/​PhysRevLett.105.070501.

[37] Mario Berta, Matthias Christandl, Roger Colbeck, Joseph M. Renes, and Renato Renner. The uncertainty principle in the presence of quantum memory. Nat. Phys., 6 (9): 659–662, September 2010. ISSN 1745-2473, 1745-2481. 10.1038/​nphys1734.

[38] Marco Tomamichel and Esther Hänggi. The link between entropic uncertainty and nonlocality. J. Phys. A: Math. Theor., 46 (5): 055301, January 2013. ISSN 1751-8121. 10.1088/​1751-8113/​46/​5/​055301.

[39] Charles Ci Wen Lim, Christopher Portmann, Marco Tomamichel, Renato Renner, and Nicolas Gisin. Device-independent quantum key distribution with local bell test. Phys. Rev. X, 3: 031006, July 2013. 10.1103/​PhysRevX.3.031006.

[40] Gilles Brassard, Norbert Lütkenhaus, Tal Mor, and Barry C. Sanders. Limitations on Practical Quantum Cryptography. Phys. Rev. Lett., 85 (6): 1330–1333, August 2000. 10.1103/​PhysRevLett.85.1330.

[41] Marcos Curty and Tobias Moroder. Heralded-qubit amplifiers for practical device-independent quantum key distribution. Phys. Rev. A, 84: 010304, July 2011. 10.1103/​PhysRevA.84.010304.

[42] Evan Meyer-Scott, Marek Bula, Karol Bartkiewicz, Antonín Černoch, Jan Soubusta, Thomas Jennewein, and Karel Lemr. Entanglement-based linear-optical qubit amplifier. Phys. Rev. A, 88: 012327, July 2013. 10.1103/​PhysRevA.88.012327.

[43] Kaushik P. Seshadreesan, Masahiro Takeoka, and Masahide Sasaki. Progress towards practical device-independent quantum key distribution with spontaneous parametric down-conversion sources, on-off photodetectors, and entanglement swapping. Phys. Rev. A, 93: 042328, April 2016. 10.1103/​PhysRevA.93.042328.

[44] David Pitkanen, Xiongfeng Ma, Ricardo Wickert, Peter van Loock, and Norbert Lütkenhaus. Efficient heralding of photonic qubits with applications to device-independent quantum key distribution. Phys. Rev. A, 84: 022325, August 2011. 10.1103/​PhysRevA.84.022325.

[45] Antonio Acín, Daniel Cavalcanti, Elsa Passaro, Stefano Pironio, and Paul Skrzypczyk. Necessary detection efficiencies for secure quantum key distribution and bound randomness. Phys. Rev. A, 93: 012319, January 2016. 10.1103/​PhysRevA.93.012319.

[46] M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl. Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide. Phys. Rev. Lett., 113: 093603, August 2014. 10.1103/​PhysRevLett.113.093603.

[47] Stephen Wein, Nikolai Lauk, Roohollah Ghobadi, and Christoph Simon. Feasibility of efficient room-temperature solid-state sources of indistinguishable single photons using ultrasmall mode volume cavities. Phys. Rev. B, 97: 205418, May 2018. 10.1103/​PhysRevB.97.205418.

[48] Chris Gustin and Stephen Hughes. Influence of electron-phonon scattering for an on-demand quantum dot single-photon source using cavity-assisted adiabatic passage. Phys. Rev. B, 96: 085305, August 2017. 10.1103/​PhysRevB.96.085305.

[49] F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, and S. W. Nam. Detecting single infrared photons with 93% system efficiency. Nat. Photonics, 7 (3): 210–214, March 2013. ISSN 1749-4893. 10.1038/​nphoton.2013.13.

[50] Jun Zhang, Mark A. Itzler, Hugo Zbinden, and Jian-Wei Pan. Advances in InGaAs/​InP single-photon detector systems for quantum communication. Light Sci. Appl., 4: e286, 2015. ISSN 2047-7538. 10.1038/​lsa.2015.59.

[51] Shigehito Miki, Masahiro Yabuno, Taro Yamashita, and Hirotaka Terai. Stable, high-performance operation of a fiber-coupled superconducting nanowire avalanche photon detector. Opt. Express, 25 (6): 6796–6804, March 2017. ISSN 1094-4087. 10.1364/​OE.25.006796.

[52] Maria Moshkova, Alexander Divochiy, Pavel Morozov, Yury Vakhtomin, Andrey Antipov, Philipp Zolotov, Vitaly Seleznev, Marat Ahmetov, and Konstantin Smirnov. High-performance superconducting photon-number-resolving detectors with 86% system efficiency at telecom range. J. Opt. Soc. Am. B, JOSAB, 36 (3): B20–B25, March 2019. 10.1364/​JOSAB.36.000B20.

[53] Lan Zhou, Yu-Bo Sheng, and Gui-Lu Long. Device-independent quantum secure direct communication against collective attacks. Science Bulletin, 65 (1): 12–20, 2020. ISSN 2095-9273. 10.1016/​j.scib.2019.10.025.

[54] Philippe Grangier, Juan Ariel Levenson, and Jean-Philippe Poizat. Quantum non-demolition measurements in optics. Nature, 396 (6711): 537–542, December 1998. ISSN 0028-0836. 10.1038/​25059.

[55] B. C. Jacobs, T. B. Pittman, and J. D. Franson. Quantum relays and noise suppression using linear optics. Phys. Rev. A, 66: 052307, November 2002. 10.1103/​PhysRevA.66.052307.

[56] Pieter Kok, Hwang Lee, and Jonathan P. Dowling. Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements. Phys. Rev. A, 66: 063814, December 2002. 10.1103/​PhysRevA.66.063814.

[57] Jian-Wei Pan, Dik Bouwmeester, Harald Weinfurter, and Anton Zeilinger. Experimental entanglement swapping: Entangling photons that never interacted. Phys. Rev. Lett., 80: 3891–3894, May 1998. 10.1103/​PhysRevLett.80.3891.

[58] S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. FHayes, L. Luo, T. A. Manning, and C. Monroe. Random numbers certified by Bell's theorem. Nature, 464, April 2010. 10.1038/​nature09008.

[59] Mikołaj Lasota, Czesław Radzewicz, Konrad Banaszek, and Rob Thew. Linear optics schemes for entanglement distribution with realistic single-photon sources. Phys. Rev. A, 90: 033836, September 2014. 10.1103/​PhysRevA.90.033836.

[60] Valerio Scarani, Helle Bechmann-Pasquinucci, Nicolas J. Cerf, Miloslav Dušek, Norbert Lütkenhaus, and Momtchil Peev. The security of practical quantum key distribution. Rev. Mod. Phys., 81: 1301–1350, September 2009. 10.1103/​RevModPhys.81.1301.

[61] Antonio Acín, Serge Massar, and Stefano Pironio. Randomness versus nonlocality and entanglement. Phys. Rev. Lett., 108: 100402, March 2012. 10.1103/​PhysRevLett.108.100402.

[62] Qiang Zhang, Xiuping Xie, Hiroki Takesue, Sae Woo Nam, Carsten Langrock, M. M. Fejer, and Yoshihisa Yamamoto. Correlated photon-pair generation in reverse-proton-exchange ppln waveguides with integrated mode demultiplexer at 10 ghz clock. Opt. Express, 15 (16): 10288–10293, August 2007. 10.1364/​oe.15.010288.

[63] Cezary Śliwa and Konrad Banaszek. Conditional preparation of maximal polarization entanglement. Phys. Rev. A, 67 (3): 030101, March 2003. 10.1103/​PhysRevA.67.030101.

[64] Stefanie Barz, Gunther Cronenberg, Anton Zeilinger, and Philip Walther. Heralded generation of entangled photon pairs. Nat. Photonics, 4 (8): 553–556, August 2010. ISSN 1749-4893. 10.1038/​nphoton.2010.156.

[65] Claudia Wagenknecht, Che-Ming Li, Andreas Reingruber, Xiao-Hui Bao, Alexander Goebel, Yu-Ao Chen, Qiang Zhang, Kai Chen, and Jian-Wei Pan. Experimental demonstration of a heralded entanglement source. Nat. Photonics, 4 (8): 549–552, August 2010. ISSN 1749-4893. 10.1038/​nphoton.2010.123.

[66] C. L. Salter, R. M. Stevenson, I. Farrer, C. A. Nicoll, D. A. Ritchie, and A. J. Shields. An entangled-light-emitting diode. Nature, 465 (7298): 594–597, June 2010. ISSN 1476-4687. 10.1038/​nature09078.

[67] R. M. Stevenson, C. L. Salter, J. Nilsson, A. J. Bennett, M. B. Ward, I. Farrer, D. A. Ritchie, and A. J. Shields. Indistinguishable Entangled Photons Generated by a Light-Emitting Diode. Phys. Rev. Lett., 108 (4): 040503, January 2012. 10.1103/​PhysRevLett.108.040503.

[68] Rinaldo Trotta, Johannes S. Wildmann, Eugenio Zallo, Oliver G. Schmidt, and Armando Rastelli. Highly Entangled Photons from Hybrid Piezoelectric-Semiconductor Quantum Dot Devices. Nano Lett., 14 (6): 3439–3444, June 2014. ISSN 1530-6984. 10.1021/​nl500968k.

[69] Le Phuc Thinh, Gonzalo de la Torre, Jean-Daniel Bancal, Stefano Pironio, and Valerio Scarani. Randomness in post-selected events. New J. Phys., 18 (3): 035007, 2016. 10.1088/​1367-2630/​18/​3/​035007.

[70] Ernest Y.-Z. Tan, Charles C.-W. Lim, and Renato Renner. Advantage distillation for device-independent quantum key distribution. Phys. Rev. Lett., 124 (2): 020502, January 2020. 10.1103/​PhysRevLett.124.020502.

[71] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden. Advances in quantum cryptography. Adv. Opt. Photonics, 2019. 10.1364/​aop.361502. URL https:/​/​​abs/​1906.01645.

[72] Víctor Zapatero and Marcos Curty. Long-distance device-independent quantum key distribution. Sci. Rep., 9, 2019. ISSN 2045-2322. 10.1038/​s41598-019-53803-0.

[73] G. Murta, S. B. van Dam, J. Ribeiro, R. Hanson, and S. Wehner. Towards a realization of device-independent quantum key distribution. Quantum Sci. Technol., 4 (3): 035011, July 2019. 10.1088/​2058-9565/​ab2819.

[74] Yoshiaki Tsujimoto, Chenglong You, Kentaro Wakui, Mikio Fujiwara, Kazuhiro Hayasaka, Shigehito Miki, Hirotaka Terai, Masahide Sasaki, Jonathan P Dowling, and Masahiro Takeoka. Heralded amplification of nonlocality via entanglement swapping. New J. Phys., 22 (2): 023008, February 2020. 10.1088/​1367-2630/​ab61da.

[75] Pieter Kok and Samuel L. Braunstein. Postselected versus nonpostselected quantum teleportation using parametric down-conversion. Phys. Rev. A, 61: 042304, March 2000. 10.1103/​PhysRevA.61.042304.

[76] Tim C. Ralph and Geoff J. Pryde. Chapter 4 - Optical Quantum Computation. In Progress in Optics, volume 54, pages 209–269. Elsevier, January 2010. 10.1016/​S0079-6638(10)05409-0.

[77] O. Nieto-Silleras, S. Pironio, and J. Silman. Using complete measurement statistics for optimal device-independent randomness evaluation. New J. Phys., 16 (1): 013035, January 2014. 10.1088/​1367-2630/​16/​1/​013035.

[78] Miguel Navascués, Stefano Pironio, and Antonio Acin. Bounding the set of quantum correlations. Phys. Rev. Lett., 98: 010401, January 2007. 10.1103/​PhysRevLett.98.010401.

[79] Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, New York, NY, USA, 2004. ISBN 0521833787. 10.1017/​cbo9780511804441.

Cited by

[1] Ravitej Uppu, Hans T. Eriksen, Henri Thyrrestrup, Aslı D. Uğurlu, Ying Wang, Sven Scholz, Andreas D. Wieck, Arne Ludwig, Matthias C. Löbl, Richard J. Warburton, Peter Lodahl, and Leonardo Midolo, "On-chip deterministic operation of quantum dots in dual-mode waveguides for a plug-and-play single-photon source", Nature Communications 11 1, 3782 (2020).

[2] Erik Woodhead, Antonio Acín, and Stefano Pironio, "Device-independent quantum key distribution with asymmetric CHSH inequalities", arXiv:2007.16146, Quantum 5, 443 (2021).

[3] Ravitej Uppu, Leonardo Midolo, Xiaoyan Zhou, Jacques Carolan, and Peter Lodahl, "Quantum-dot-based deterministic photon–emitter interfaces for scalable photonic quantum technology", Nature Nanotechnology (2021).

[4] Qingshan Xu, Xiaoqing Tan, Rui Huang, and Xiaodan Zeng, "Parallel self‐testing for device‐independent verifiable blind quantum computation", Quantum Engineering 2 3(2020).

[5] Simon Milz, Dario Egloff, Philip Taranto, Thomas Theurer, Martin B. Plenio, Andrea Smirne, and Susana F. Huelga, "When Is a Non-Markovian Quantum Process Classical?", Physical Review X 10 4, 041049 (2020).

[6] Ravitej Uppu, Freja T. Pedersen, Ying Wang, Cecilie T. Olesen, Camille Papon, Xiaoyan Zhou, Leonardo Midolo, Sven Scholz, Andreas D. Wieck, Arne Ludwig, and Peter Lodahl, "Scalable integrated single-photon source", Science Advances 6 50, eabc8268 (2020).

[7] Ali Motazedifard, Seyed Ahmad Madani, and N. S. Vayaghan, "Measurement of entropy and quantum coherence properties of two type-I entangled photonic qubits", Optical and Quantum Electronics 53 7, 378 (2021).

[8] René Schwonnek, Koon Tong Goh, Ignatius W. Primaatmaja, Ernest Y.-Z. Tan, Ramona Wolf, Valerio Scarani, and Charles C.-W. Lim, "Device-independent quantum key distribution with random key basis", Nature Communications 12 1, 2880 (2021).

[9] G. Murta, S. B. van Dam, J. Ribeiro, R. Hanson, and S. Wehner, "Towards a realization of device-independent quantum key distribution", Quantum Science and Technology 4 3, 035011 (2019).

[10] Camille Papon, Xiaoyan Zhou, Henri Thyrrestrup, Zhe Liu, Søren Stobbe, Rüdiger Schott, Andreas D. Wieck, Arne Ludwig, Peter Lodahl, and Leonardo Midolo, "Nanomechanical single-photon routing", Optica 6 4, 524 (2019).

[11] Víctor Zapatero and Marcos Curty, "Long-distance device-independent quantum key distribution", Scientific Reports 9, 17749 (2019).

[12] Sumanta Das, Liang Zhai, Mantas Čepulskovskis, Alisa Javadi, Sahand Mahmoodian, Peter Lodahl, and Anders S. Sørensen, "A wave-function ansatz method for calculating field correlations and its application to the study of spectral filtering and quantum dynamics of multi-emitter systems", arXiv:1912.08303.

[13] Yu-Fei Yan, Lan Zhou, Wei Zhong, and Yu-Bo Sheng, "Measurement-device-independent quantum key distribution of multiple degrees of freedom of a single photon", Frontiers of Physics 16 1, 11501 (2020).

[14] Peter J. Brown, Sammy Ragy, and Roger Colbeck, "A framework for quantum-secure device-independent randomness expansion", arXiv:1810.13346.

[15] Yoshiaki Tsujimoto, Chenglong You, Kentaro Wakui, Mikio Fujiwara, Kazuhiro Hayasaka, Shigehito Miki, Hirotaka Terai, Masahide Sasaki, Jonathan P. Dowling, and Masahiro Takeoka, "Heralded amplification of nonlocality via entanglement swapping", New Journal of Physics 22 2, 023008 (2020).

[16] Hélène Ollivier, Ilse Maillette de Buy Wenniger, Sarah Thomas, Stephen Wein, Guillaume Coppola, Abdelmounaim Harouri, Paul Hilaire, Clément Millet, Aristide Lemaître, Isabelle Sagnes, Olivier Krebs, Loïc Lanco, Juan Carlos Loredo, Carlos Antón, Niccolo Somaschi, and Pascale Senellart, "Reproducibility of high-performance quantum dot single-photon sources", arXiv:1910.08863.

The above citations are from Crossref's cited-by service (last updated successfully 2021-10-19 18:21:44) and SAO/NASA ADS (last updated successfully 2021-10-19 18:21:45). The list may be incomplete as not all publishers provide suitable and complete citation data.