Device-independent quantum key distribution with asymmetric CHSH inequalities

Erik Woodhead1,2, Antonio Acín2, and Stefano Pironio1

1Laboratoire d'Information Quantique, CP 225, Université libre de Bruxelles (ULB), Av. F. D. Roosevelt 50, 1050 Bruxelles, Belgium
2ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

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Abstract

The simplest device-independent quantum key distribution protocol is based on the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality and allows two users, Alice and Bob, to generate a secret key if they observe sufficiently strong correlations. There is, however, a mismatch between the protocol, in which only one of Alice's measurements is used to generate the key, and the CHSH expression, which is symmetric with respect to Alice's two measurements. We therefore investigate the impact of using an extended family of Bell expressions where we give different weights to Alice's measurements. Using this family of asymmetric Bell expressions improves the robustness of the key distribution protocol for certain experimentally-relevant correlations. As an example, the tolerable error rate improves from 7.15% to about 7.42% for the depolarising channel. Adding random noise to Alice's key before the postprocessing pushes the threshold further to more than 8.34%. The main technical result of our work is a tight bound on the von Neumann entropy of one of Alice's measurement outcomes conditioned on a quantum eavesdropper for the family of asymmetric CHSH expressions we consider and allowing for an arbitrary amount of noise preprocessing.

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Cited by

[1] Pavel Sekatski, Jean-Daniel Bancal, Xavier Valcarce, Ernest Y.-Z. Tan, Renato Renner, and Nicolas Sangouard, "Device-independent quantum key distribution from generalized CHSH inequalities", arXiv:2009.01784, Quantum 5, 444 (2021).

[2] Peter Brown, Hamza Fawzi, and Omar Fawzi, "Computing conditional entropies for quantum correlations", Nature Communications 12, 575 (2021).

[3] Ernest Y. -Z. Tan, Pavel Sekatski, Jean-Daniel Bancal, René Schwonnek, Renato Renner, Nicolas Sangouard, and Charles C. -W. Lim, "Improved DIQKD protocols with finite-size analysis", arXiv:2012.08714.

[4] Máté Farkas, Maria Balanzó-Juandó, Karol Łukanowski, Jan Kołodyński, and Antonio Acín, "Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols", arXiv:2103.02639.

[5] Xavier Valcarce, Julian Zivy, Nicolas Sangouard, and Pavel Sekatski, "Self-testing two-qubit maximally entangled states from generalized CHSH tests", arXiv:2011.03047.

[6] Junior R. Gonzales-Ureta, Ana Predojević, and Adán Cabello, "Device-independent quantum key distribution based on Bell inequalities with more than two inputs and two outputs", arXiv:2104.00413.

The above citations are from Crossref's cited-by service (last updated successfully 2021-05-06 15:31:56) and SAO/NASA ADS (last updated successfully 2021-05-06 15:31:57). The list may be incomplete as not all publishers provide suitable and complete citation data.