Semi-device-independent framework based on natural physical assumptions

Thomas Van Himbeeck1,2, Erik Woodhead3, Nicolas J. Cerf2, Raúl García-Patrón2, and Stefano Pironio1

1Laboratoire d’Information Quantique, Université libre de Bruxelles (ULB), Belgium
2Centre for Quantum Information and Communication, Universit´e libre de Bruxelles (ULB), Belgium
3ICFO - Institut de Cíencies Fotóniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

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

Abstract

The semi-device-independent approach provides a framework for prepare-and-measure quantum protocols using devices whose behavior must not be characterized nor trusted, except for a single assumption on the dimension of the Hilbert space characterizing the quantum carriers. Here, we propose instead to constrain the quantum carriers through a bound on the mean value of a well-chosen observable. This modified assumption is physically better motivated than a dimension bound and closer to the description of actual experiments. In particular, we consider quantum optical schemes where the source emits quantum states described in an infinite-dimensional Fock space and model our assumption as an upper bound on the average photon number in the emitted states. We characterize the set of correlations that may be exhibited in the simplest possible scenario compatible with our new framework, based on two energy-constrained state preparations and a two-outcome measurement. Interestingly, we uncover the existence of quantum correlations exceeding the set of classical correlations that can be produced by devices behaving in a purely pre-determined fashion (possibly including shared randomness). This feature suggests immediate applications to certified randomness generation. Along this line, we analyze the achievable correlations in several prepare-and-measure optical schemes with a mean photon number constraint and demonstrate that they allow for the generation of certified randomness. Our simplest optical scheme works by the on-off keying of an attenuated laser source followed by photocounting. It opens the path to more sophisticated energy-constrained semi-device-independent quantum cryptography protocols, such as quantum key distribution.

► BibTeX data

► References

[1] D. Mayers and A. Yao, in Proceedings of the 39th Annual Symposium on Foundations of Computer Science (IEEE Computer Society, Los Alamitos, 1998) pp. 503–509, arXiv:quant-ph/​9809039.
https:/​/​doi.org/​10.1109/​SFCS.1998.743501
arXiv:quant-ph/9809039

[2] J. Barrett, L. Hardy, and A. Kent, Physical Review Letters 95, 010503 (2005), arXiv:quant-ph/​0405101.
https:/​/​doi.org/​10.1103/​PhysRevLett.95.010503
arXiv:quant-ph/0405101

[3] R. Colbeck, Quantum And Relativistic Protocols For Secure Multi-Party Computation, Ph.D. thesis, University of Cambridge (2006), arXiv:0911.3814 [quant-ph].
arXiv:0911.3814

[4] R. Colbeck and A. Kent, Journal of Physics A 44, 095305 (2011), arXiv:1011.4474 [quant-ph].
https:/​/​doi.org/​10.1088/​1751-8113/​44/​9/​095305
arXiv:1011.4474

[5] A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Physical Review Letters 98, 230501 (2007), arXiv:quant-ph/​0702152.
https:/​/​doi.org/​10.1103/​PhysRevLett.98.230501
arXiv:quant-ph/0702152

[6] B. W. Reichardt, F. Unger, and U. Vazirani, Nature 496, 456 (2013), arXiv:1209.0448 [quant-ph].
https:/​/​doi.org/​10.1038/​nature12035
arXiv:1209.0448

[7] C. A. Miller and Y. Shi, in Proceedings of the 46th Annual ACM Symposium on Theory of Computing, STOC '14 (ACM, New York, NY, USA, 2014) pp. 417–426, arXiv:1402.0489 [quant-ph].
https:/​/​doi.org/​10.1145/​2591796.2591843
arXiv:1402.0489

[8] R. Arnon-Friedman, R. Renner, and T. Vidick, Simple and tight device-independent security proofs, (2016), arXiv:1607.01797 [quant-ph].
arXiv:1607.01797

[9] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Reviews of Modern Physics 86, 419 (2014), arXiv:1303.2849 [quant-ph].
https:/​/​doi.org/​10.1103/​RevModPhys.86.419
arXiv:1303.2849

[10] N. Brunner, S. Pironio, A. Acín, N. Gisin, A. A. Méthot, and V. Scarani, Physical Review Letters 100, 210503 (2008), arXiv:0802.0760 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevLett.100.210503
arXiv:0802.0760

[11] R. Gallego, N. Brunner, C. Hadley, and A. Acín, Physical Review Letters 105, 230501 (2010), arXiv:1010.5064 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevLett.105.230501
arXiv:1010.5064

[12] J. Bowles, M. T. Quintino, and N. Brunner, Physical Review Letters 112, 140407 (2014), arXiv:1311.1525 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevLett.112.140407
arXiv:1311.1525

[13] T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, Physical Review Letters 114, 150501 (2015), arXiv:1410.2790 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevLett.114.150501
arXiv:1410.2790

[14] M. Pawłowski and N. Brunner, Physical Review A 84, 010302(R) (2011), arXiv:1103.4105 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevA.84.010302
arXiv:1103.4105

[15] E. Woodhead and S. Pironio, Physical Review Letters 115, 150501 (2015), arXiv:1507.02889 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevLett.115.150501
arXiv:1507.02889

[16] J. Ahrens, P. Badziag, A. Cabello, and M. Bourennane, Nature Physics 8, 592 (2012), arXiv:1111.1277 [quant-ph].
https:/​/​doi.org/​10.1038/​nphys2333
arXiv:1111.1277

[17] M. Hendrych, R. Gallego, M. Mičuda, N. Brunner, A. Acín, and J. P. Torres, Nature Physics 8, 588 (2012), arXiv:1111.1208 [quant-ph].
https:/​/​doi.org/​10.1038/​nphys2334
arXiv:1111.1208

[18] B. S. Tsirel'son, Journal of Soviet Mathematics 36, 557 (1987).
https:/​/​doi.org/​10.1007/​BF01663472

[19] R. F. Werner and M. M. Wolf, Physical Review A 64, 032112 (2001), arXiv:quant-ph/​0102024.
https:/​/​doi.org/​10.1103/​PhysRevA.64.032112
arXiv:quant-ph/0102024

[20] L. Masanes, Necessary and sufficient condition for quantum-generated correlations, (2003), arXiv:quant-ph/​0309137.
arXiv:quant-ph/0309137

[21] R. Cleve, P. Hoyer, B. Toner, and J. Watrous, in Proc. Annu. IEEE Conf. Comput. Complex. (IEEE, 2004) pp. 236–249, arXiv:quant-ph/​0404076.
https:/​/​doi.org/​10.1109/​CCC.2004.1313847
arXiv:quant-ph/0404076

[22] M. Navascués, S. Pironio, and A. Acín, Phys. Rev. Lett. 98, 010401 (2007), arXiv:quant-ph/​0607119.
https:/​/​doi.org/​10.1103/​PhysRevLett.98.010401
arXiv:quant-ph/0607119

[23] M. Navascués, S. Pironio, and A. Acín, New Journal of Physics 10, 073013 (2008), arXiv:0803.4290 [quant-ph].
https:/​/​doi.org/​10.1088/​1367-2630/​10/​7/​073013
arXiv:0803.4290

[24] A. C. Doherty, B. Toner, Y. C. Liang, and S. Wehner, in Proc. Annu. IEEE Conf. Comput. Complex. (IEEE, 2008) pp. 199–210, arXiv:0803.4373 [quant-ph].
https:/​/​doi.org/​10.1109/​CCC.2008.26
arXiv:0803.4373

[25] N. Brunner, M. Navascués, and T. Vértesi, Physical Review Letters 110, 150501 (2013), arXiv:1209.5643 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevLett.110.150501
arXiv:1209.5643

[26] M. Navascues and T. Vertési, Physical Review Letters 115, 020501 (2015), arXiv:1412.0924 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevLett.115.020501
arXiv:1412.0924

[27] T. Van Himbeeck et al., in preparation.

[28] B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, Physical Review X 5, 041009 (2015), arXiv:1503.00662 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevX.5.041009
arXiv:1503.00662

[29] J. Barrett, A. Kent, and S. Pironio, Physical Review Letters 97, 170409 (2006), arXiv:quant-ph/​0605182.
https:/​/​doi.org/​10.1103/​PhysRevLett.97.170409
arXiv:quant-ph/0605182

[30] 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 C. Monroe, Nature 464, 1021 (2010), arXiv:0911.3427 [quant-ph].
https:/​/​doi.org/​10.1038/​nature09008
arXiv:0911.3427

[31] S. Pironio and S. Massar, Physical Review A 87, 012336 (2013), arXiv:1111.6056 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevA.87.012336
arXiv:1111.6056

[32] O. Nieto-Silleras, C. Bamps, J. Silman, and S. Pironio, Device-independent randomness generation from several Bell estimators, (2016), arXiv:1611.00352 [quant-ph].
arXiv:1611.00352

[33] R. Chaves, J. B. Brask, and N. Brunner, Physical Review Letters 115, 110501 (2015), arXiv:1505.07802 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevLett.115.110501
arXiv:1505.07802

[34] J. Silman, S. Pironio, and S. Massar, Physical Review Letters 110, 100504 (2013), arXiv:1211.5921 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevLett.110.100504
arXiv:1211.5921

[35] J. B. Brask, A. Martin, W. Esposito, R. Houlmann, J. Bowles, H. Zbinden, and N. Brunner, Physical Review A 7, 054018 (2017), arXiv:1612.06566 [quant-ph].
https:/​/​doi.org/​10.1103/​PhysRevApplied.7.054018
arXiv:1612.06566

Cited by

[1] Davide Rusca, Thomas van Himbeeck, Anthony Martin, Jonatan Bohr Brask, Stefano Pironio, Nicolas Brunner, and Hugo Zbinden, Quantum Information and Measurement (QIM) V: Quantum Technologies S1B.3 (2019) ISBN:978-1-943580-56-9.

[2] Yanbao Zhang, Emanuel Knill, and Peter Bierhorst, "Certifying quantum randomness by probability estimation", Physical Review A 98 4, 040304 (2018).

[3] P. R. Smith, D. G. Marangon, M. Lucamarini, Z. L. Yuan, and A. J. Shields, "Simple source device-independent continuous-variable quantum random number generator", Physical Review A 99 6, 062326 (2019).

[4] Armin Tavakoli, Massimiliano Smania, Tamás Vértesi, Nicolas Brunner, and Mohamed Bourennane, "Self-testing nonprojective quantum measurements in prepare-and-measure experiments", Science Advances 6 16, eaaw6664 (2020).

[5] Davide Rusca, Hamid Tebyanian, Anthony Martin, and Hugo Zbinden, "Fast self-testing quantum random number generator based on homodyne detection", Applied Physics Letters 116 26, 264004 (2020).

[6] Armin Tavakoli, Jędrzej Kaniewski, Tamás Vértesi, Denis Rosset, and Nicolas Brunner, "Self-testing quantum states and measurements in the prepare-and-measure scenario", Physical Review A 98 6, 062307 (2018).

[7] Mathieu Bozzio, Eleni Diamanti, and Frédéric Grosshans, "Semi-device-independent quantum money with coherent states", Physical Review A 99 2, 022336 (2019).

[8] Marie Ioannou, Jonatan Bohr Brask, and Nicolas Brunner, "Upper bound on certifiable randomness from a quantum black-box device", Physical Review A 99 5, 052338 (2019).

[9] Thibault Michel, Jing Yan Haw, Davide G. Marangon, Oliver Thearle, Giuseppe Vallone, Paolo Villoresi, Ping Koy Lam, and Syed M. Assad, "Real-Time Source-Independent Quantum Random-Number Generator with Squeezed States", Physical Review Applied 12 3, 034017 (2019).

[10] Alastair A Abbott, Cristian S Calude, Michael J Dinneen, and Nan Huang, "Experimentally probing the algorithmic randomness and incomputability of quantum randomness", Physica Scripta 94 4, 045103 (2019).

[11] Jiajun Ma, Aishwarya Hakande, Xiao Yuan, and Xiongfeng Ma, "Coherence as a resource for source-independent quantum random-number generation", Physical Review A 99 2, 022328 (2019).

[12] Li Liu, Yukun Wang, Emilien Lavie, Chao Wang, Arno Ricou, Fen Zhuo Guo, and Charles Ci Wen Lim, "Practical Quantum Key Distribution with Non-Phase-Randomized Coherent States", Physical Review Applied 12 2, 024048 (2019).

[13] J. Cariñe, G. Cañas, P. Skrzypczyk, I. Šupić, N. Guerrero, T. Garcia, L. Pereira, M. A. S. Prosser, G. B. Xavier, A. Delgado, S. P. Walborn, D. Cavalcanti, and G. Lima, "Multi-core fiber integrated multi-port beam splitters for quantum information processing", Optica 7 5, 542 (2020).

[14] Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Jonatan Bohr Brask, Nicolas Gisin, and Nicolas Brunner, "Informationally restricted quantum correlations", Quantum 4, 332 (2020).

[15] Yukun Wang, Ignatius William Primaatmaja, Emilien Lavie, Antonios Varvitsiotis, and Charles Ci Wen Lim, "Characterising the correlations of prepare-and-measure quantum networks", npj Quantum Information 5 1, 17 (2019).

[16] Davide Rusca, Thomas van Himbeeck, Anthony Martin, Jonatan Bohr Brask, Weixu Shi, Stefano Pironio, Nicolas Brunner, and Hugo Zbinden, "Self-testing quantum random-number generator based on an energy bound", Physical Review A 100 6, 062338 (2019).

[17] Weixu Shi, Yu Cai, Jonatan Bohr Brask, Hugo Zbinden, and Nicolas Brunner, "Semi-device-independent characterization of quantum measurements under a minimum overlap assumption", Physical Review A 100 4, 042108 (2019).

[18] Marco Avesani, Davide G. Marangon, Giuseppe Vallone, and Paolo Villoresi, "Source-device-independent heterodyne-based quantum random number generator at 17 Gbps", Nature Communications 9 1, 5365 (2018).

[19] Nicolò Leone, Davide Rusca, Stefano Azzini, Giorgio Fontana, Fabio Acerbi, Alberto Gola, Alessandro Tontini, Nicola Massari, Hugo Zbinden, and Lorenzo Pavesi, "An optical chip for self-testing quantum random number generation", APL Photonics 5 10, 101301 (2020).

[20] Brian Coyle, Elham Kashefi, and Matty J. Hoban, "Certified Randomness From Steering Using Sequential Measurements", Cryptography 3 4, 27 (2019).

[21] Andrew J. P. Garner, Marius Krumm, and Markus P. Müller, "Semi-device-independent information processing with spatiotemporal degrees of freedom", Physical Review Research 2 1, 013112 (2020).

[22] Jonatan Bohr Brask, Anthony Martin, William Esposito, Raphael Houlmann, Joseph Bowles, Hugo Zbinden, and Nicolas Brunner, "Megahertz-Rate Semi-Device-Independent Quantum Random Number Generators Based on Unambiguous State Discrimination", arXiv:1612.06566, Physical Review Applied 7 5, 054018 (2017).

[23] Matej Pivoluska, Martin Plesch, Máté Farkas, Natália Ružičková, Clara Flegel, Natalia Herrera Valencia, Will McCutcheon, Mehul Malik, and Edgar A. Aguilar, "Semi-Device-Independent Random Number Generation with Flexible Assumptions", arXiv:2002.12295.

The above citations are from Crossref's cited-by service (last updated successfully 2020-10-19 11:29:14) and SAO/NASA ADS (last updated successfully 2020-10-19 11:29:15). The list may be incomplete as not all publishers provide suitable and complete citation data.