Device-independent quantum key distribution from generalized CHSH inequalities

Pavel Sekatski; Jean-Daniel Bancal; Xavier Valcarce; Ernest Y.-Z. Tan; Renato Renner; Nicolas Sangouard

doi:10.22331/q-2021-04-26-444

Device-independent quantum key distribution from generalized CHSH inequalities

Pavel Sekatski¹, Jean-Daniel Bancal², Xavier Valcarce³, Ernest Y.-Z. Tan⁴, Renato Renner⁴, and Nicolas Sangouard^1,3

¹Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
²Department of Applied Physics, University of Geneva, Chemin de Pinchat 22, 1211 Geneva, Switzerland
³Université Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191, Gif-sur-Yvette, France
⁴Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland

Published:	2021-04-26, volume 5, page 444
Eprint:	arXiv:2009.01784v4
Doi:	https://doi.org/10.22331/q-2021-04-26-444
Citation:	Quantum 5, 444 (2021).

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

Abstract

Device-independent quantum key distribution aims at providing security guarantees even when using largely uncharacterised devices. In the simplest scenario, these guarantees are derived from the CHSH score, which is a simple linear combination of four correlation functions. We here derive a security proof from a generalisation of the CHSH score, which effectively takes into account the individual values of two correlation functions. We show that this additional information, which is anyway available in practice, allows one to get higher key rates than with the CHSH score. We discuss the potential advantage of this technique for realistic photonic implementations of device-independent quantum key distribution.

Popular summary

Device-independent quantum key distribution aims to distribute a secure key with devices that are largely uncharacterized and untrusted. Although it provides high security guarantees, the implementation of device-independent quantum key distribution is demanding in terms of experimental resources. For example, a source producing strongly entangled signals is needed to efficiently bound the eavesdropper information. The relevant measure of entanglement is the amount by which the measurement statistics violate a Bell inequality, such as the Clauser-Horne-Shimony-Holt (CHSH) inequality. Intuitively, a significant violation of this inequality guarantees that Alice and Bob’s state is close to a two-qubit maximally entangled state which cannot be shared with a third party. This, in turn, guarantees that information available to Eve –- the eavesdropper — about Alice and Bob’s measurement outcomes is bounded.
We here derive a security proof from generalisations of the CHSH inequality. While these generalisations exploit the same results than the standard CHSH test and are thus not more difficult to test in practice, we show that they allow one to get higher key rates than with the CHSH score while there are not more demanding in practice. We discuss the potential advantage of this technique for realistic photonic implementations of device-independent quantum key distribution.

► BibTeX data

@article{Sekatski2021deviceindependent,
  doi = {10.22331/q-2021-04-26-444},
  url = {https://doi.org/10.22331/q-2021-04-26-444},
  title = {Device-independent quantum key distribution from generalized {CHSH} inequalities},
  author = {Sekatski, Pavel and Bancal, Jean-Daniel and Valcarce, Xavier and Tan, Ernest Y.-Z. and Renner, Renato and Sangouard, Nicolas},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {444},
  month = apr,
  year = {2021}
}

► References

[1] Artur K. Ekert ``Quantum cryptography based on Bell's theorem'' Phys. Rev. Lett. 67, 661-663 (1991).
https://doi.org/10.1103/PhysRevLett.67.661

[2] 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

[3] Igor Devetakand Andreas Winter ``Distillation of secret key and entanglement from quantum states'' Proc. R. Soc. Lond. A 461, 207–235 (2005).
https://doi.org/10.1098/rspa.2004.1372

[4] Antonio Acín, Nicolas Gisin, and Lluis Masanes, ``From Bell's Theorem to Secure Quantum Key Distribution'' Phys. Rev. Lett. 97, 120405 (2006).
https://doi.org/10.1103/PhysRevLett.97.120405

[5] Yi Zhao, Chi-Hang Fred Fung, Bing Qi, Christine Chen, and Hoi-Kwong Lo, ``Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems'' Phys. Rev. A 78, 042333 (2008).
https://doi.org/10.1103/PhysRevA.78.042333

[6] Lars Lydersen, Carlos Wiechers, Christoffer Wittmann, Dominique Elser, Johannes Skaar, and Vadim Makarov, ``Hacking commercial quantum cryptography systems by tailored bright illumination'' Nature Photonics 4, 686–689 (2010).
https://doi.org/10.1038/nphoton.2010.214

[7] Henning Weier, Harald Krauss, Markus Rau, Martin Fürst, Sebastian Nauerth, and Harald Weinfurter, ``Quantum eavesdropping without interception: an attack exploiting the dead time of single-photon detectors'' New Journal of Physics 13, 073024 (2011).
https://doi.org/10.1088/1367-2630/13/7/073024

[8] Juan Carlos Garcia-Escartin, Shihan Sajeed, and Vadim Makarov, ``Attacking quantum key distribution by light injection via ventilation openings'' preprint arXiv:1910.08152 (2019).
https://doi.org/10.1371/journal.pone.0236630

[9] Samuel L. Braunsteinand Stefano Pirandola ``Side-Channel-Free Quantum Key Distribution'' Phys. Rev. Lett. 108, 130502 (2012).
https://doi.org/10.1103/PhysRevLett.108.130502

[10] Hoi-Kwong Lo, Marcos Curty, and Bing Qi, ``Measurement-Device-Independent Quantum Key Distribution'' Phys. Rev. Lett. 108, 130503 (2012).
https://doi.org/10.1103/PhysRevLett.108.130503

[11] A. Rubenok, J. A. Slater, P. Chan, I. Lucio-Martinez, and W. Tittel, ``Real-World Two-Photon Interference and Proof-of-Principle Quantum Key Distribution Immune to Detector Attacks'' Phys. Rev. Lett. 111, 130501 (2013).
https://doi.org/10.1103/PhysRevLett.111.130501

[12] T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, ``Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits'' Phys. Rev. A 88, 052303 (2013).
https://doi.org/10.1103/PhysRevA.88.052303

[13] Yang Liu, Teng-Yun Chen, Liu-Jun Wang, Hao Liang, Guo-Liang Shentu, Jian Wang, Ke Cui, Hua-Lei Yin, Nai-Le Liu, Li Li, Xiongfeng Ma, Jason S. Pelc, M. M. Fejer, Cheng-Zhi Peng, Qiang Zhang, and Jian-Wei Pan, ``Experimental Measurement-Device-Independent Quantum Key Distribution'' Phys. Rev. Lett. 111, 130502 (2013).
https://doi.org/10.1103/PhysRevLett.111.130502

[14] Zhiyuan Tang, Zhongfa Liao, Feihu Xu, Bing Qi, Li Qian, and Hoi-Kwong Lo, ``Experimental Demonstration of Polarization Encoding Measurement-Device-Independent Quantum Key Distribution'' Phys. Rev. Lett. 112, 190503 (2014).
https://doi.org/10.1103/PhysRevLett.112.190503

[15] L. Comandar, M. Lucamarini, and B. et al. Fröhlich, ``Quantum key distribution without detector vulnerabilities using optically seeded lasers'' Nature Photon 10, 312–315 (2016).
https://doi.org/10.1038/nphoton.2016.50

[16] Xavier Valcarce, Julian Zivy, Nicolas Sangouard, and Pavel Sekatski, ``Self-testing two-qubit maximally entangled states from generalized CHSH tests'' preprint arXiv:2011.03047 (2020).

[17] Rene Schwonnek, Koon Tong Goh, Ignatius W. Primaatmaja, Ernest Y.-Z. Tan, Ramona Wolf, Valerio Scarani, and Charles C.-W. Lim, ``Robust Device-Independent Quantum Key Distribution'' preprint arXiv:2005.02691 (2020).

[18] 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

[19] Camille Jordan ``Essai sur la géométrie à $ n $ dimensions'' Bulletin de la Société mathématique de France 3, 103–174 (1875).

[20] Ivan Šupićand Joseph Bowles ``Self-testing of quantum systems: a review'' Quantum 4, 337 (2020).
https://doi.org/10.22331/q-2020-09-30-337

[21] Stefano Pironio, Antonio Acin, Nicolas Brunner, Nicolas Gisin, Serge Massar, and Valerio Scarani, ``Device-independent quantum key distribution secure against collective attacks'' New Journal of Physics 11, 045021 (2009).
https://doi.org/10.1088/1367-2630/11/4/045021

[22] M. Ho, P. Sekatski, E. Y.-Z. Tan, R. Renner, J.-D. Bancal, and N. Sangouard, ``Noisy Preprocessing Facilitates a Photonic Realization of Device-Independent Quantum Key Distribution'' Phys. Rev. Lett. 124, 230502 (2020).
https://doi.org/10.1103/PhysRevLett.124.230502

[23] Renato Renner, Nicolas Gisin, and Barbara Kraus, ``Information-theoretic security proof for quantum-key-distribution protocols'' Physical Review A 72, 012332 (2005).
https://doi.org/10.1103/PhysRevA.72.012332

[24] B. Kraus, N. Gisin, and R. Renner, ``Lower and Upper Bounds on the Secret-Key Rate for Quantum Key Distribution Protocols Using One-Way Classical Communication'' Phys. Rev. Lett. 95, 080501 (2005).
https://doi.org/10.1103/PhysRevLett.95.080501

[25] Joseph M. Renesand Graeme Smith ``Noisy Processing and Distillation of Private Quantum States'' Phys. Rev. Lett. 98, 020502 (2007).
https://doi.org/10.1103/PhysRevLett.98.020502

[26] Erik Woodhead, Antonio Acín, and Stefano Pironio, ``Device-independent quantum key distribution based on asymmetric CHSH inequalities'' preprint arXiv:2007.16146 (2020).

[27] 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 preprint arXiv:2012.08714 (2020).

[28] Michael A. Nielsenand Isaac L. Chuang ``Quantum Computation and Quantum Information: 10th Anniversary Edition'' Cambridge University Press (2011).

[29] Xavier Valcarce, Pavel Sekatski, Davide Orsucci, Enky Oudot, Jean-Daniel Bancal, and Nicolas Sangouard, ``What is the minimum CHSH score certifying that a state resembles the singlet?'' Quantum 4, 246 (2020).
https://doi.org/10.22331/q-2020-03-23-246

[30] Marissa Giustina, Alexandra Mech, Sven Ramelow, Bernhard Wittmann, Johannes Kofler, Jörn Beyer, Adriana Lita, Brice Calkins, Thomas Gerrits, and Sae Woo Nam, ``Bell violation using entangled photons without the fair-sampling assumption'' Nature 497, 227 (2013).
https://doi.org/10.1038/nature12012

[31] BG Christensen, KT McCusker, JB Altepeter, B Calkins, Thomas Gerrits, Adriana E Lita, A Miller, Lynden K Shalm, Y Zhang, and SW Nam, ``Detection-loophole-free test of quantum nonlocality, and applications'' Physical review letters 111, 130406 (2013).
https://doi.org/10.1103/PhysRevLett.111.130406

[32] Lynden K Shalm, Evan Meyer-Scott, Bradley G Christensen, Peter Bierhorst, Michael A Wayne, Martin J Stevens, Thomas Gerrits, Scott Glancy, Deny R Hamel, and Michael S Allman, ``Strong loophole-free test of local realism'' Physical review letters 115, 250402 (2015).
https://doi.org/10.1103/PhysRevLett.115.250402

[33] Marissa Giustina, Marijn AM Versteegh, Sören Wengerowsky, Johannes Handsteiner, Armin Hochrainer, Kevin Phelan, Fabian Steinlechner, Johannes Kofler, Jan-Åke Larsson, and Carlos Abellán, ``Significant-loophole-free test of Bell’s theorem with entangled photons'' Physical review letters 115, 250401 (2015).
https://doi.org/10.1103/PhysRevLett.115.250401

[34] Lijiong Shen, Jianwei Lee, Jean-Daniel Bancal, Alessandro Cerè, Antia Lamas-Linares, Adriana Lita, Thomas Gerrits, Sae Woo Nam, Valerio Scarani, and Christian Kurtsiefer, ``Randomness extraction from bell violation with continuous parametric down-conversion'' Physical review letters 121, 150402 (2018).
https://doi.org/10.1103/PhysRevLett.121.150402

[35] Yang Liu, Qi Zhao, Ming-Han Li, Jian-Yu Guan, Yanbao Zhang, Bing Bai, Weijun Zhang, Wen-Zhao Liu, Cheng Wu, and Xiao Yuan, ``Device-independent quantum random-number generation'' Nature 562, 548 (2018).
https://doi.org/10.1038/s41586-018-0559-3

[36] Philippe H. Eberhard ``Background level and counter efficiencies required for a loophole-free Einstein-Podolsky-Rosen experiment'' Phys. Rev. A 47, R747–R750 (1993).
https://doi.org/10.1103/PhysRevA.47.R747

[37] Xiongfeng Maand Norbert Lütkenhaus ``Improved Data Post-Processing in Quantum Key Distribution and Application to Loss Thresholds in device independent QKD'' Quantum Inf. Comput. 12, 203–214 (2012).
https://doi.org/10.26421/QIC12.3-4

[38] Alexey A. Melnikov, Pavel Sekatski, and Nicolas Sangouard, ``Setting Up Experimental Bell Tests with Reinforcement Learning'' Phys. Rev. Lett. 125, 160401 (2020).
https://doi.org/10.1103/PhysRevLett.125.160401

[39] Erik Woodhead ``Tight asymptotic key rate for the Bennett-Brassard 1984 protocol with local randomization and device imprecisions'' Phys. Rev. A 90, 022306 (2014).
https://doi.org/10.1103/PhysRevA.90.022306

[40] L. Mirsky ``A trace inequality of John von Neumann'' Monatshefte für Mathematik 79, 303–306 (1975).
https://doi.org/10.1007/bf01647331

Cited by

[1] Yang Xiang, "Multipartite quantum cryptography based on the violation of Svetlichny’s inequality", The European Physical Journal D 77 2, 31 (2023).

[2] Michael Liaofan Liu, Florian Kanitschar, Amir Arqand, and Ernest Y.-Z. Tan, "Lipschitz continuity of quantum-classical conditional entropies with respect to angular distance and related properties", Physical Review A 107 2, 022426 (2023).

[3] Alexey Melnikov, Mohammad Kordzanganeh, Alexander Alodjants, and Ray-Kuang Lee, "Quantum machine learning: from physics to software engineering", Advances in Physics: X 8 1, 2165452 (2023).

[4] Thomas A. Hahn and Ernest Y.-Z. Tan, "Fidelity bounds for device-independent advantage distillation", npj Quantum Information 8 1, 145 (2022).

[5] Ramona Wolf, Lecture Notes in Physics 988, 159 (2021) ISBN:978-3-030-73990-4.

[6] 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", Physical Review Letters 127 5, 050503 (2021).

[7] Marie Ioannou, Maria Ana Pereira, Davide Rusca, Fadri Grünenfelder, Alberto Boaron, Matthieu Perrenoud, Alastair A. Abbott, Pavel Sekatski, Jean-Daniel Bancal, Nicolas Maring, Hugo Zbinden, and Nicolas Brunner, "Receiver-Device-Independent Quantum Key Distribution", Quantum 6, 718 (2022).

[8] Eva M. González-Ruiz, Sumanta K. Das, Peter Lodahl, and Anders S. Sørensen, "Violation of Bell's inequality with quantum-dot single-photon sources", Physical Review A 106 1, 012222 (2022).

[9] Karol Łukanowski, Máté Farkas, Maria Balanzó-Juandó, Antonio Acín, and Jan Kołodyński, Quantum 2.0 Conference and Exhibition QTu4C.1 (2022) ISBN:978-1-957171-11-1.

[10] Emanuel-Cristian Boghiu, Flavien Hirsch, Pei-Sheng Lin, Marco Túlio Quintino, and Joseph Bowles, "Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios", SciPost Physics Core 6 2, 028 (2023).

[11] Feihu Xu, Yu-Zhe Zhang, Qiang Zhang, and Jian-Wei Pan, "Device-Independent Quantum Key Distribution with Random Postselection", Physical Review Letters 128 11, 110506 (2022).

[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 7920, 682 (2022).

[13] 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", Physical Review A 103 5, 052436 (2021).

[14] Thinh P. Le, Chiara Meroni, Bernd Sturmfels, Reinhard F. Werner, and Timo Ziegler, "Quantum Correlations in the Minimal Scenario", Quantum 7, 947 (2023).

[15] 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", Physical Review Letters 129 5, 050502 (2022).

[16] 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", Quantum 6, 880 (2022).

[17] Federico Grasselli, Gláucia Murta, Hermann Kampermann, and Dagmar Bruß, "Boosting device-independent cryptography with tripartite nonlocality", Quantum 7, 980 (2023).

[18] Víctor Zapatero, Tim van Leent, Rotem Arnon-Friedman, Wen-Zhao Liu, Qiang Zhang, Harald Weinfurter, and Marcos Curty, "Advances in device-independent quantum key distribution", npj Quantum Information 9 1, 10 (2023).

[19] 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).

[20] Xavier Valcarce, Julian Zivy, Nicolas Sangouard, and Pavel Sekatski, "Self-testing two-qubit maximally entangled states from generalized Clauser-Horne-Shimony-Holt tests", Physical Review Research 4 1, 013049 (2022).

[21] Rutvij Bhavsar, Sammy Ragy, and Roger Colbeck, "Improved device-independent randomness expansion rates using two sided randomness", arXiv:2103.07504, (2021).

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

[23] Emanuel-Cristian Boghiu, Flavien Hirsch, Pei-Sheng Lin, Marco Túlio Quintino, and Joseph Bowles, "Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios", arXiv:2111.06358, (2021).

The above citations are from Crossref's cited-by service (last updated successfully 2023-06-07 05:21:14) and SAO/NASA ADS (last updated successfully 2023-06-07 05:21:15). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.