Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks

Karol Łukanowski1,2, Maria Balanzó-Juandó3, Máté Farkas4,3, Antonio Acín3,5, and Jan Kołodyński1

1Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warszawa, Poland
2Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland
3ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain
4Department of Mathematics, University of York, Heslington, York, YO10 5DD, United Kingdom
5ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain

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Abstract

The device-independent framework constitutes the most pragmatic approach to quantum protocols that does not put any trust in their implementations. It requires all claims, about e.g. security, to be made at the level of the final classical data in hands of the end-users. This imposes a great challenge for determining attainable key rates in $\textit{device-independent quantum key distribution}$ (DIQKD), but also opens the door for consideration of eavesdropping attacks that stem from the possibility of a given data being just generated by a malicious third-party. In this work, we explore this path and present the $\textit{convex-combination attack}$ as an efficient, easy-to-use technique for upper-bounding DIQKD key rates. It allows verifying the accuracy of lower bounds on key rates for state-of-the-art protocols, whether involving one-way or two-way communication. In particular, we demonstrate with its help that the currently predicted constraints on the robustness of DIQKD protocols to experimental imperfections, such as the finite visibility or detection efficiency, are already very close to the ultimate tolerable thresholds.

The device-independent framework constitutes the most pragmatic approach to quantum cryptography that does not put any trust in its implementation. In principle, it allows the end-users to securely distribute cryptographic keys even when the vendor providing the devices behaves maliciously. However, this comes at the price of very stringent requirements on the quality of the data observed, which must then exhibit correlations that cannot be explained by means of classical physics. So far, it has been uncertain whether these demanding conditions cannot be relaxed solely by improving the security proofs. Thanks to our work, we now know that this is not the case—there exists a simple attack to be explored by a potential eavesdropper that can nearly always be successfully performed, unless the stringent requirements on data-quality are indeed fulfilled.

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[1] Ignatius W. Primaatmaja, Koon Tong Goh, Ernest Y. -Z. Tan, John T. -F. Khoo, Shouvik Ghorai, and Charles C. -W. Lim, "Security of device-independent quantum key distribution protocols: a review", Quantum 7, 932 (2023).

[2] Giuseppe Viola, Nikolai Miklin, Mariami Gachechiladze, and Marcin Pawłowski, "Entanglement witnessing with untrusted detectors", Journal of Physics A Mathematical General 56 42, 425301 (2023).

[3] Eva M. González-Ruiz, Javier Rivera-Dean, Marina F. B. Cenni, Anders S. Sørensen, Antonio Acín, and Enky Oudot, "Device Independent Quantum Key Distribution with realistic single-photon source implementations", arXiv:2211.16472, (2022).

[4] Hong-Yi Su, "Monte Carlo approach to the evaluation of the security of device-independent quantum key distribution", New Journal of Physics 25 12, 123036 (2023).

[5] Yu-Zhe Zhang, Yi-Zheng Zhen, and Feihu Xu, "Upper bound on device-independent quantum key distribution with two way classical postprocessing under individual attack", New Journal of Physics 24 11, 113045 (2022).

[6] Javier Rivera-Dean, Anna Steffinlongo, Neil Parker-Sánchez, Antonio Acín, and Enky Oudot, "Device-Independent Quantum Key Distribution beyond qubits", arXiv:2402.00161, (2024).

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