A coherence-witnessing game and applications to semi-device-independent quantum key distribution

Mário Silva1, Ricardo Faleiro2, Paulo Mateus2,3, and Emmanuel Zambrini Cruzeiro2

1Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
2Instituto de Telecomunicações, 1049-001, Lisbon, Portugal
3Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais 1049-001, Lisbon, Portugal

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Abstract

Semi-device-independent quantum key distribution aims to achieve a balance between the highest level of security, device independence, and experimental feasibility. Semi-quantum key distribution presents an intriguing approach that seeks to minimize users' reliance on quantum operations while maintaining security, thus enabling the development of simplified and hardware fault-tolerant quantum protocols. In this work, we introduce a coherence-based, semi-device-independent, semi-quantum key distribution protocol built upon a noise-robust version of a coherence equality game that witnesses various types of coherence. Security is proven in the bounded quantum storage model, requiring users to implement only classical operations, specifically fixed-basis detections.

Device-independent cryptography aims to establish security with minimal assumptions about the devices used. Alternatively, the goal of the semi-quantum perspective is to reduce users' reliance on quantum operations while still ensuring security based on the principles of quantum mechanics. In this work, we extend a coherence equality game to a noise-robust scenario and demonstrate its capability to statistically differentiate between three types of coherence resources: non-coherent, separable coherent, and entangled coherent states. Building upon the game, we present a proof-of-concept quantum key distribution protocol. In this protocol, Alice and Bob only need to perform trusted particle detections within their labs, while the remaining components of the protocol are considered untrusted. Consequently, this protocol can be accurately characterized as both semi-device-independent and semi-quantum, showcasing the compatibility of both frameworks.

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► References

[1] M. S. Sharbaf. ``Quantum cryptography: An emerging technology in network security''. 2011 IEEE International Conference on Technologies for Homeland Security (HST)Pages 13–19 (2011).
https:/​/​doi.org/​10.1109/​THS.2011.6107841

[2] Peter W. Shor. ``Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer''. SIAM J. Comput., 26(5), 1484–1509 (1997).
https:/​/​doi.org/​10.1137/​S0097539795293172

[3] Charles H. Bennett and Gilles Brassard. ``Quantum cryptography: Public key distribution and coin tossing''. Theoretical Computer Science 560, 7–11 (2014).
https:/​/​doi.org/​10.1016/​j.tcs.2014.05.025

[4] Dominic Mayers and Andrew Yao. ``Quantum cryptography with imperfect apparatus''. Proceedings of the 39th Annual Symposium on Foundations of Computer Science (1998).

[5] Dominic Mayers and Andrew Yao. ``Self testing quantum apparatus''. Quantum Info. Comput. 4, 273–286 (2004).

[6] Umesh Vazirani and Thomas Vidick. ``Fully device-independent quantum key distribution''. Physical Review Letters 113 (2014).
https:/​/​doi.org/​10.1103/​physrevlett.113.140501

[7] Rotem Arnon-Friedman, Frédéric Dupuis, Omar Fawzi, Renato Renner, and Thomas Vidick. ``Practical device-independent quantum cryptography via entropy accumulation''. Nature Communications 9, 459 (2018).
https:/​/​doi.org/​10.1038/​s41467-017-02307-4

[8] S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and et al. ``Random numbers certified by bell’s theorem''. Nature 464, 1021–1024 (2010).
https:/​/​doi.org/​10.1038/​nature09008

[9] Antonio Acín, Serge Massar, and Stefano Pironio. ``Randomness versus nonlocality and entanglement''. Phys. Rev. Lett. 108, 100402 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.108.100402

[10] Nati Aharon, André Chailloux, Iordanis Kerenidis, Serge Massar, Stefano Pironio, and Jonathan Silman. ``Weak coin flipping in a device-independent setting''. In Revised Selected Papers of the 6th Conference on Theory of Quantum Computation, Communication, and Cryptography - Volume 6745, pg.1–12. TQC 2011 (2011).
https:/​/​doi.org/​10.1007/​978-3-642-54429-3_1

[11] Ricardo Faleiro and Manuel Goulão. ``Device-independent quantum authorization based on the Clauser-Horne-Shimony-Holt game''. Phys. Rev. A 103, 022430 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.103.022430

[12] D. P. Nadlinger, P. Drmota, B. C. Nichol, G. Araneda, D. Main, R. Srinivas, D. M. Lucas, C. J. Ballance, K. Ivanov, E. Y.-Z. Tan, P. Sekatski, R. L. Urbanke, R. Renner, N. Sangouard, and J.-D. Bancal. ``Experimental quantum key distribution certified by bell's theorem''. Nature 607, 682–686 (2022).
https:/​/​doi.org/​10.1038/​s41586-022-04941-5

[13] Wei Zhang, Tim van Leent, Kai Redeker, Robert Garthoff, René Schwonnek, Florian Fertig, Sebastian Eppelt, Wenjamin Rosenfeld, Valerio Scarani, Charles C.-W. Lim, and Harald Weinfurter. ``A device-independent quantum key distribution system for distant users''. Nature 607, 687–691 (2022).
https:/​/​doi.org/​10.1038/​s41586-022-04891-y

[14] Wen-Zhao Liu, Yu-Zhe Zhang, Yi-Zheng Zhen, Ming-Han Li, Yang Liu, Jingyun Fan, Feihu Xu, Qiang Zhang, and Jian-Wei Pan. ``Toward a photonic demonstration of device-independent quantum key distribution''. Phys. Rev. Lett. 129, 050502 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.129.050502

[15] Marcin Pawłowski and Nicolas Brunner. ``Semi-device-independent security of one-way quantum key distribution''. Phys. Rev. A 84, 010302 (2011).
https:/​/​doi.org/​10.1103/​PhysRevA.84.010302

[16] Anubhav Chaturvedi, Maharshi Ray, Ryszard Veynar, and Marcin Pawłowski. ``On the security of semi-device-independent QKD protocols''. Quantum Information Processing 17, 131 (2018).
https:/​/​doi.org/​10.1007/​s11128-018-1892-z

[17] Armin Tavakoli, Jędrzej Kaniewski, Tamás Vértesi, Denis Rosset, and Nicolas Brunner. ``Self-testing quantum states and measurements in the prepare-and-measure scenario''. Phys. Rev. A 98, 062307 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.062307

[18] Armin Tavakoli. ``Semi-device-independent certification of independent quantum state and measurement devices''. Phys. Rev. Lett. 125, 150503 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.150503

[19] Thomas Van Himbeeck, Erik Woodhead, Nicolas J. Cerf, Raúl García-Patrón, and Stefano Pironio. ``Semi-device-independent framework based on natural physical assumptions''. Quantum 1, 33 (2017).
https:/​/​doi.org/​10.22331/​q-2017-11-18-33

[20] Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Erik Woodhead, and Stefano Pironio. ``Informationally restricted correlations: a general framework for classical and quantum systems''. Quantum 6, 620 (2022).
https:/​/​doi.org/​10.22331/​q-2022-01-05-620

[21] Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Erik Woodhead, and Stefano Pironio. ``Informationally restricted correlations: a general framework for classical and quantum systems''. Quantum 6, 620 (2022).
https:/​/​doi.org/​10.22331/​q-2022-01-05-620

[22] Weixu Shi, Yu Cai, Jonatan Bohr Brask, Hugo Zbinden, and Nicolas Brunner. ``Semi-device-independent characterization of quantum measurements under a minimum overlap assumption''. Phys. Rev. A 100, 042108 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.042108

[23] Hasan Iqbal and Walter O. Krawec. ``Semi-quantum cryptography''. Quantum Information Processing 19, 97 (2020).
https:/​/​doi.org/​10.1007/​s11128-020-2595-9

[24] Michel Boyer, Ran Gelles, Dan Kenigsberg, and Tal Mor. ``Semiquantum key distribution''. Phys. Rev. A 79, 032341 (2009).
https:/​/​doi.org/​10.1103/​PhysRevA.79.032341

[25] Francesco Massa, Preeti Yadav, Amir Moqanaki, Walter O. Krawec, Paulo Mateus, Nikola Paunković, André Souto, and Philip Walther. ``Experimental Semi-quantum Key Distribution With Classical Users''. Quantum 6, 819 (2022).
https:/​/​doi.org/​10.22331/​q-2022-09-22-819

[26] Flavio Del Santo and Borivoje Dakić. ``Coherence equality and communication in a quantum superposition''. Physical Review Letters 124 (2020).
https:/​/​doi.org/​10.1103/​physrevlett.124.190501

[27] Lieven Vandenberghe and Stephen Boyd. ``Semidefinite programming''. SIAM Rev. 38, 49–95 (1996).
https:/​/​doi.org/​10.1137/​1038003

[28] Károly F. Pál and Tamás Vértesi. ``Efficiency of higher-dimensional hilbert spaces for the violation of bell inequalities''. Phys. Rev. A 77, 042105 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.77.042105

[29] Matthew McKague, Michele Mosca, and Nicolas Gisin. ``Simulating quantum systems using real hilbert spaces''. Phys. Rev. Lett. 102, 020505 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.102.020505

[30] K. C. Toh, M. J. Todd, and R. H. Tütüncü. ``Sdpt3 — a matlab software package for semidefinite programming, version 1.3''. Optimization Methods and Software 11, 545–581 (1999).
https:/​/​doi.org/​10.1080/​10556789908805762

[31] Reinhard F. Werner and Michael M. Wolf. ``Bell inequalities and entanglement'' (2001). arXiv:quant-ph/​0107093.
arXiv:quant-ph/0107093

[32] J. Lofberg. ``Yalmip : a toolbox for modeling and optimization in matlab''. In 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508). Pages 284–289. (2004).
https:/​/​doi.org/​10.1109/​CACSD.2004.1393890

[33] Sébastien Designolle, Roope Uola, Kimmo Luoma, and Nicolas Brunner. ``Set coherence: Basis-independent quantification of quantum coherence''. Phys. Rev. Lett. 126, 220404 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.220404

[34] Rafael Wagner, Rui Soares Barbosa, and Ernesto F. Galvão. ``Inequalities witnessing coherence, nonlocality, and contextuality'' (2023). arXiv:2209.02670.
arXiv:2209.02670

[35] Kazuoki Azuma. ``Weighted sums of certain dependent random variables''. Tohoku Math. J. (2) 19, 357–367 (1967).
https:/​/​doi.org/​10.2748/​tmj/​1178243286

[36] Renato Renner. ``Security of quantum key distribution''. International Journal of Quantum Information 6, 1–127 (2008).
https:/​/​doi.org/​10.1142/​S0219749908003256

[37] Robert Konig, Renato Renner, and Christian Schaffner. ``The operational meaning of min- and max-entropy''. IEEE Transactions on Information Theory 55, 4337–4347 (2009).
https:/​/​doi.org/​10.1109/​tit.2009.2025545

Cited by

[1] Julia Guskind and Walter O. Krawec, "Mediated semi-quantum key distribution with improved efficiency", Quantum Science and Technology 7 3, 035019 (2022).

[2] Saachi Mutreja and Walter O. Krawec, "Improved semi-quantum key distribution with two almost-classical users", Quantum Information Processing 21 9, 319 (2022).

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