Informationally restricted correlations: a general framework for classical and quantum systems

Armin Tavakoli1,2, Emmanuel Zambrini Cruzeiro3, Erik Woodhead3, and Stefano Pironio3

1Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
2Institute for Quantum Optics and Quantum Information – IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
3Laboratoire d'Information Quantique, CP 225, Université libre de Bruxelles (ULB), Av. F. D. Roosevelt 50, 1050 Bruxelles, Belgium

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

Abstract

We introduce new methods and tools to study and characterise classical and quantum correlations emerging from prepare-and-measure experiments with informationally restricted communication. We consider the most general kind of informationally restricted correlations, namely the ones formed when the sender is allowed to prepare statistical mixtures of mixed states, showing that contrary to what happens in Bell nonlocality, mixed states can outperform pure ones. We then leverage these tools to derive device-independent witnesses of the information content of quantum communication, witnesses for different quantum information resources, and demonstrate that these methods can be used to develop a new avenue for semi-device independent random number generators.

► BibTeX data

► References

[1] A. Ambainis, A. Nayak, A. Ta-Shma, and U. Vazirani, in Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, STOC '99 (Association for Computing Machinery, New York, NY, USA, 1999) pp. 376–383.
https:/​/​doi.org/​10.1145/​301250.301347

[2] E. F. Galvão, Phys. Rev. A 65, 012318 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.65.012318

[3] P. Trojek, C. Schmid, M. Bourennane, C. Brukner, M. Zukowski, and H. Weinfurter, Phys. Rev. A 72, 050305 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.72.050305

[4] A. Ambainis, D. Leung, L. Mancinska, and M. Ozols, Quantum random access codes with shared randomness (2008), arXiv:0810.2937 [quant-ph].
arXiv:0810.2937

[5] R. Gallego, N. Brunner, C. Hadley, and A. Acín, Phys. Rev. Lett. 105, 230501 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.105.230501

[6] N. Brunner, M. Navascués, and T. Vértesi, Phys. Rev. Lett. 110, 150501 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.150501

[7] A. Tavakoli, A. Hameedi, B. Marques, and M. Bourennane, Phys. Rev. Lett. 114, 170502 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.114.170502

[8] M. Navascués and T. Vértesi, Phys. Rev. Lett. 115, 020501 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.020501

[9] M. Smania, A. M. Elhassan, A. Tavakoli, and M. Bourennane, npj Quantum Inf. 2, 16010 (2016).
https:/​/​doi.org/​10.1038/​npjqi.2016.10

[10] A. Tavakoli and M. Żukowski, Phys. Rev. A 95, 042305 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.042305

[11] D. Martínez, A. Tavakoli, M. Casanova, G. Cañas, B. Marques, and G. Lima, Phys. Rev. Lett. 121, 150504 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.150504

[12] N. Brunner, S. Pironio, A. Acin, N. Gisin, A. A. Méthot, and V. Scarani, Phys. Rev. Lett. 100, 210503 (2008).
https:/​/​doi.org/​10.1103/​PhysRevLett.100.210503

[13] M. Pawłowski and N. Brunner, Phys. Rev. A 84, 010302 (2011).
https:/​/​doi.org/​10.1103/​PhysRevA.84.010302

[14] H.-W. Li, Z.-Q. Yin, Y.-C. Wu, X.-B. Zou, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, Phys. Rev. A 84, 034301 (2011a).
https:/​/​doi.org/​10.1103/​PhysRevA.84.034301

[15] E. Woodhead and S. Pironio, Phys. Rev. Lett. 115, 150501 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.150501

[16] A. Tavakoli, J. Kaniewski, T. Vértesi, D. Rosset, and N. Brunner, Phys. Rev. A 98, 062307 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.062307

[17] T. Van Himbeeck, E. Woodhead, N. J. Cerf, R. García-Patrón, and S. Pironio, Quantum 1, 33 (2017).
https:/​/​doi.org/​10.22331/​q-2017-11-18-33

[18] J. B. Brask, A. Martin, W. Esposito, R. Houlmann, J. Bowles, H. Zbinden, and N. Brunner, Phys. Rev. Applied 7, 054018 (2017).
https:/​/​doi.org/​10.1103/​PhysRevApplied.7.054018

[19] R. Chaves, J. B. Brask, and N. Brunner, Phys. Rev. Lett. 115, 110501 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.110501

[20] A. Tavakoli, Phys. Rev. Lett. 126, 210503 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.210503

[21] A. Tavakoli, E. Zambrini Cruzeiro, J. B. Brask, N. Gisin, and N. Brunner, Quantum 4, 332 (2020).
https:/​/​doi.org/​10.22331/​q-2020-09-24-332

[22] R. Konig, R. Renner, and C. Schaffner, IEEE Trans. Inf. Th. 55, 4337 (2009).
https:/​/​doi.org/​10.1109/​TIT.2009.2025545

[23] N. Ciganović, N. J. Beaudry, and R. Renner, IEEE Trans. Inf. Th. 60, 1573 (2013).
https:/​/​doi.org/​10.1109/​TIT.2013.2295314

[24] A. Tavakoli, J. Pauwels, E. Woodhead, and S. Pironio, Correlations in entanglement-assisted prepare-and-measure scenarios (2021), arXiv:2103.10748v2, 2103.10748.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.040357
arXiv:2103.10748

[25] L. Wang and R. Renner, Phys. Rev. Lett. 108, 200501 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.108.200501

[26] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.419

[27] S. Lörwald and G. Reinelt, EURO J. Comput. Optim. 3, 297 (2015).
https:/​/​doi.org/​10.1007/​s13675-015-0040-0

[28] R. F. Werner and M. M. Wolf, Quantum Inf. Comput. 1, 1 (2001).

[29] K. F. Pál and T. Vértesi, Phys. Rev. A 82, 022116 (2010).
https:/​/​doi.org/​10.1103/​PhysRevA.82.022116

[30] A. Tavakoli, M. Pawłowski, M. Żukowski, and M. Bourennane, Phys. Rev. A 95, 020302 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.020302

[31] J. Watrous, The Theory of Quantum Information (Cambridge University Press, 2018).

[32] S. Burgdorf, K. Cafuta, I. Klep, and J. Povh, Mathematical Programming 137, 557 (2013).
https:/​/​doi.org/​10.1007/​s10107-011-0505-8

[33] I. Klep and J. Povh, Journal of Global Optimization 64, 325 (2016).
https:/​/​doi.org/​10.1007/​s10898-015-0308-1

[34] M. Navascués, S. Pironio, and A. Acín, New J. Phys. 10, 073013 (2008), publisher: IOP Publishing.
https:/​/​doi.org/​10.1088/​1367-2630/​10/​7/​073013

[35] S. Pironio, M. Navascués, and A. Acín, SIAM J. Opt. 20, 2157 (2010), publisher: Society for Industrial and Applied Mathematics.
https:/​/​doi.org/​10.1137/​090760155

[36] S. Gribling, D. de Laat, and M. Laurent, Foundations of Computational Mathematics 19, 1013 (2019).
https:/​/​doi.org/​10.1007/​s10208-018-09410-y

[37] J. Ahrens, P. Badziag, A. Cabello, and M. Bourennane, Nat. Phys. 8, 592 (2012).
https:/​/​doi.org/​10.1038/​nphys2333

[38] H.-W. Li, Z.-Q. Yin, Y.-C. Wu, X.-B. Zou, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, Phys. Rev. A 84, 034301 (2011b).
https:/​/​doi.org/​10.1103/​PhysRevA.84.034301

[39] H.-W. Li, M. Pawłowski, Z.-Q. Yin, G.-C. Guo, and Z.-F. Han, Phys. Rev. A 85, 052308 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.85.052308

[40] A. Tavakoli, D. Rosset, and M.-O. Renou, Phys. Rev. Lett. 122, 070501 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.070501

Cited by

[1] Armin Tavakoli, Alejandro Pozas-Kerstjens, Ming-Xing Luo, and Marc-Olivier Renou, "Bell nonlocality in networks", arXiv:2104.10700.

[2] Armin Tavakoli, "Semi-Device-Independent Framework Based on Restricted Distrust in Prepare-and-Measure Experiments", Physical Review Letters 126 21, 210503 (2021).

[3] Tony Metger, Yfke Dulek, Andrea Coladangelo, and Rotem Arnon-Friedman, "Device-independent quantum key distribution from computational assumptions", New Journal of Physics 23 12, 123021 (2021).

[4] Armin Tavakoli, Jef Pauwels, Erik Woodhead, and Stefano Pironio, "Correlations in Entanglement-Assisted Prepare-and-Measure Scenarios", PRX Quantum 2 4, 040357 (2021).

[5] Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Roope Uola, and Alastair A. Abbott, "Bounding and Simulating Contextual Correlations in Quantum Theory", PRX Quantum 2 2, 020334 (2021).

[6] Ming-Xing Luo, "Network configuration theory for all networks", arXiv:2107.05846.

[7] George Moreno, Ranieri Nery, Carlos de Gois, Rafael Rabelo, and Rafael Chaves, "Semi-device-independent certification of entanglement in superdense coding", Physical Review A 103 2, 022426 (2021).

[8] Anubhav Chaturvedi, Marcin Pawłowski, and Debashis Saha, "Quantum description of reality is empirically incomplete", arXiv:2110.13124.

[9] Jef Pauwels, Armin Tavakoli, Erik Woodhead, and Stefano Pironio, "Entanglement in prepare-and-measure scenarios: many questions, a few answers", arXiv:2108.00442.

The above citations are from SAO/NASA ADS (last updated successfully 2022-01-23 06:40:52). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2022-01-23 06:40:49).