Boosting device-independent cryptography with tripartite nonlocality

Federico Grasselli, Gláucia Murta, Hermann Kampermann, and Dagmar Bruß

Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany

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Device-independent (DI) protocols, such as DI conference key agreement (DICKA) and DI randomness expansion (DIRE), certify private randomness by observing nonlocal correlations when two or more parties test a Bell inequality. While most DI protocols are restricted to bipartite Bell tests, harnessing multipartite nonlocal correlations may lead to better performance. Here, we consider tripartite DICKA and DIRE protocols based on testing multipartite Bell inequalities, specifically: the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality, and the Holz and the Parity-CHSH inequalities introduced in the context of DICKA protocols. We evaluate the asymptotic performance of the DICKA (DIRE) protocols in terms of their conference key rate (net randomness generation rate), by deriving lower bounds on the conditional von Neumann entropy of one party's outcome and two parties' outcomes. For the Holz inequality, we prove a tight analytical lower bound on the one-outcome entropy and conjecture a tight lower bound on the two-outcome entropy. We additionally re-derive the analytical one-outcome entropy bound for the MABK inequality with a much simpler method and obtain a numerical lower bound on the two-outcome entropy for the Parity-CHSH inequality. Our simulations show that DICKA and DIRE protocols employing tripartite Bell inequalities can significantly outperform their bipartite counterparts. Moreover, we establish that genuine multipartite entanglement is not a precondition for multipartite DIRE while its necessity for DICKA remains an open question.

In device-independent protocols, the amount of secret randomness that can be certified depends on the nonlocality of the observed correlations, quantified by the violation of a Bell inequality. Most device-independent protocols are based on the violation of bipartite Bell inequalities (e.g. the CHSH inequality). In our work, we show that multipartite nonlocal correlations, testified by the violation of multipartite Bell inequalities, enable the certification of more secret randomness from the outcomes of one or two parties. This is achieved by deriving analytical and numerical bounds on the relevant conditional von Neumann entropies.

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[1] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden. ``Advances in quantum cryptography''. Adv. Opt. Photon. 12, 1012–1236 (2020).

[2] Feihu Xu, Xiongfeng Ma, Qiang Zhang, Hoi-Kwong Lo, and Jian-Wei Pan. ``Secure quantum key distribution with realistic devices''. Rev. Mod. Phys. 92, 025002 (2020).

[3] 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).

[4] Ilja Gerhardt, Qin Liu, Antía Lamas-Linares, Johannes Skaar, Christian Kurtsiefer, and Vadim Makarov. ``Full-field implementation of a perfect eavesdropper on a quantum cryptography system''. Nature Communications 2, 349 (2011).

[5] A. Yao and D. Mayers. ``Quantum cryptography with imperfect apparatus''. In IEEE 54th Annual Symposium on Foundations of Computer Science. Page 503. Los Alamitos, CA, USA (1998). IEEE Computer Society.

[6] Antonio Acín, Nicolas Gisin, and Lluis Masanes. ``From bell's theorem to secure quantum key distribution''. Phys. Rev. Lett. 97, 120405 (2006).

[7] Jonathan Barrett, Adrian Kent, and Stefano Pironio. ``Maximally nonlocal and monogamous quantum correlations''. Phys. Rev. Lett. 97, 170409 (2006).

[8] J. S. Bell and Alain Aspect. ``Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy''. Cambridge University Press. (2004). 2 edition.

[9] Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. ``Bell nonlocality''. Rev. Mod. Phys. 86, 419–478 (2014).

[10] B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, 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 (2015).

[11] 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 (2015).

[12] 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 (2007).

[13] Stefano Pironio, Antonio Acín, 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).

[14] Lluís Masanes, Stefano Pironio, and Antonio Acín. ``Secure device-independent quantum key distribution with causally independent measurement devices''. Nature Communications 2, 238 (2011).

[15] Umesh Vazirani and Thomas Vidick. ``Fully device-independent quantum key distribution''. Phys. Rev. Lett. 113, 140501 (2014).

[16] 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).

[17] Valerio Scarani and Nicolas Gisin. ``Quantum communication between n partners and bell's inequalities''. Phys. Rev. Lett. 87, 117901 (2001).

[18] Valerio Scarani and Nicolas Gisin. ``Quantum key distribution between n partners: Optimal eavesdropping and bell's inequalities''. Phys. Rev. A 65, 012311 (2001).

[19] Timo Holz, Hermann Kampermann, and Dagmar Bruß. ``Genuine multipartite bell inequality for device-independent conference key agreement''. Phys. Rev. Research 2, 023251 (2020).

[20] Jérémy Ribeiro, Gláucia Murta, and Stephanie Wehner. ``Reply to ``comment on fully device-independent conference key agreement''''. Phys. Rev. A 100, 026302 (2019).

[21] Gláucia Murta, Federico Grasselli, Hermann Kampermann, and Dagmar Bruß. ``Quantum conference key agreement: A review''. Advanced Quantum Technologies 3, 2000025 (2020).

[22] Roger Colbeck. ``Quantum and relativistic protocols for secure multi-party computation'' (2011). arXiv:0911.3814.

[23] 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, et al. ``Random numbers certified by bell's theorem''. Nature 464, 1021–1024 (2010).

[24] Roger Colbeck and Adrian Kent. ``Private randomness expansion with untrusted devices''. Journal of Physics A: Mathematical and Theoretical 44, 095305 (2011).

[25] Carl A. Miller and Yaoyun Shi. ``Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices''. J. ACM 63 (2016).

[26] Stefano Pironio and Serge Massar. ``Security of practical private randomness generation''. Phys. Rev. A 87, 012336 (2013).

[27] Serge Fehr, Ran Gelles, and Christian Schaffner. ``Security and composability of randomness expansion from bell inequalities''. Phys. Rev. A 87, 012335 (2013).

[28] Erik Woodhead, Boris Bourdoncle, and Antonio Acín. ``Randomness versus nonlocality in the Mermin-Bell experiment with three parties''. Quantum 2, 82 (2018).

[29] Wen-Zhao Liu, Ming-Han Li, Sammy Ragy, Si-Ran Zhao, Bing Bai, Yang Liu, Peter J. Brown, Jun Zhang, Roger Colbeck, Jingyun Fan, Qiang Zhang, and Jian-Wei Pan. ``Device-independent randomness expansion against quantum side information''. Nature Physics 17, 448–451 (2021).

[30] Lynden K. Shalm, Yanbao Zhang, Joshua C. Bienfang, Collin Schlager, Martin J. Stevens, Michael D. Mazurek, Carlos Abellán, Waldimar Amaya, Morgan W. Mitchell, Mohammad A. Alhejji, Honghao Fu, Joel Ornstein, Richard P. Mirin, Sae Woo Nam, and Emanuel Knill. ``Device-independent randomness expansion with entangled photons''. Nature Physics 17, 452–456 (2021).

[31] 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).

[32] 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).

[33] 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).

[34] 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 (1969).

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

[36] Michele Masini, Stefano Pironio, and Erik Woodhead. ``Simple and practical DIQKD security analysis via BB84-type uncertainty relations and pauli correlation constraints''. Quantum 6, 843 (2022).

[37] 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''. Quantum 5, 444 (2021).

[38] Rutvij Bhavsar, Sammy Ragy, and Roger Colbeck. ``Improved device-independent randomness expansion rates using two sided randomness'' (2023). arXiv:2103.07504.

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

[40] Ernest Y.-Z. Tan, René Schwonnek, Koon Tong Goh, Ignatius William Primaatmaja, and Charles C.-W. Lim. ``Computing secure key rates for quantum cryptography with untrusted devices''. npj Quantum Information 7, 158 (2021).

[41] 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).

[42] N. David Mermin. ``Extreme quantum entanglement in a superposition of macroscopically distinct states''. Phys. Rev. Lett. 65, 1838–1840 (1990).

[43] M. Ardehali. ``Bell inequalities with a magnitude of violation that grows exponentially with the number of particles''. Phys. Rev. A 46, 5375–5378 (1992).

[44] A. V. Belinskiĭ and D. N. Klyshko. ``Interference of light and bell's theorem''. Phys. Rev. A 36, 653–693 (1993).

[45] Antonio Acín, Serge Massar, and Stefano Pironio. ``Randomness versus nonlocality and entanglement''. Phys. Rev. Lett. 108, 100402 (2012).

[46] Jérémy Ribeiro, Gláucia Murta, and Stephanie Wehner. ``Fully device-independent conference key agreement''. Phys. Rev. A 97, 022307 (2018).

[47] Federico Grasselli, Gláucia Murta, Hermann Kampermann, and Dagmar Bruß. ``Entropy bounds for multiparty device-independent cryptography''. PRX Quantum 2, 010308 (2021).

[48] Lluís Masanes. ``Asymptotic violation of bell inequalities and distillability''. Phys. Rev. Lett. 97, 050503 (2006).

[49] Mario Berta, Matthias Christandl, Roger Colbeck, Joseph M. Renes, and Renato Renner. ``The uncertainty principle in the presence of quantum memory''. Nature Physics 6, 659–662 (2010).

[50] Timo Holz, Daniel Miller, Hermann Kampermann, and Dagmar Bruß. ``Comment on ``fully device-independent conference key agreement''''. Phys. Rev. A 100, 026301 (2019).

[51] Federico Grasselli. ``Quantum cryptography''. Springer International Publishing. (2021).

[52] 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, 035011 (2019).

[53] Jonathan Barrett, Roger Colbeck, and Adrian Kent. ``Memory attacks on device-independent quantum cryptography''. Phys. Rev. Lett. 110, 010503 (2013).

[54] F. Dupuis and O. Fawzi. ``Entropy accumulation with improved second-order term''. IEEE Transactions on Information Theory 65, 7596–7612 (2019).

[55] Alexander Pickston, Joseph Ho, Andrés Ulibarrena, Federico Grasselli, Massimiliano Proietti, Christopher L. Morrison, Peter Barrow, Francesco Graffitti, and Alessandro Fedrizzi. ``Experimental network advantage for quantum conference key agreement'' (2022). arXiv:2207.01643.

[56] Michael Epping, Hermann Kampermann, Chiara Macchiavello, and Dagmar Bruß. ``Multi-partite entanglement can speed up quantum key distribution in networks''. New Journal of Physics 19, 093012 (2017).

[57] Giacomo Carrara, Hermann Kampermann, Dagmar Bruß, and Glá ucia Murta. ``Genuine multipartite entanglement is not a precondition for secure conference key agreement''. Physical Review Research 3 (2021).

[58] Michael A. Nielsen and Isaac L. Chuang. ``Quantum computation and quantum information: 10th anniversary edition''. Cambridge University Press. (2010).

[59] Lucas Tendick, Hermann Kampermann, and Dagmar Bruß. ``Quantifying necessary quantum resources for nonlocality''. Physical Review Research 4 (2022).

[60] Wolfram Research, Inc. ``Mathematica, Version 10.3'' (2016).

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[1] Youwang Xiao, Zong Wang, Wen‐Na Zhao, and Ming Li, "Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator", Advanced Quantum Technologies 2400101 (2024).

[2] Ekta Panwar, Palash Pandya, and Marcin Wieśniak, "An elegant scheme of self-testing for multipartite Bell inequalities", npj Quantum Information 9 1, 71 (2023).

[3] Peter Brown, Hamza Fawzi, and Omar Fawzi, "Device-independent lower bounds on the conditional von Neumann entropy", arXiv:2106.13692, (2021).

[4] Lewis Wooltorton, Peter Brown, and Roger Colbeck, "Expanding bipartite Bell inequalities for maximum multi-partite randomness", arXiv:2308.07030, (2023).

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