Informationally restricted quantum correlations

Armin Tavakoli1, Emmanuel Zambrini Cruzeiro1, Jonatan Bohr Brask2, Nicolas Gisin1, and Nicolas Brunner1

1Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
2Department of Physics, Technical University of Denmark, Fysikvej, 2800 Kongens Lyngby, Denmark

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Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content of the quantum communication, rather than on its Hilbert-space dimension. Specifically, we explore the extent of classical and quantum correlations given an upper bound on the one-shot accessible information. We provide a characterisation of the set of classical correlations and show that quantum correlations are stronger than classical ones. We also show that limiting information rather than dimension leads to stronger quantum correlations. Moreover, we present device-independent tests for placing lower bounds on the information given observed correlations. Finally, we show that quantum communication carrying $\log d$ bits of information is at least as strong a resource as $d$-dimensional classical communication assisted by pre-shared entanglement.

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[1] H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, Nonlocality and communication complexity, Rev. Mod. Phys. 82, 665 (2010).

[2] H. Buhrman, R. Cleve and A. Wigderson, Quantum vs. classical communication and computation, Proceedings of the 30th Annual ACM Symposium on Theory of Computin, 63 (1998).

[3] R. Raz, Exponential separation of quantum and classical communication complexity, In Proceedings of 31st ACM STOC, 358 (1999).

[4] R. Gallego, N. Brunner, C. Hadley, and A. Acín, Device-Independent Tests of Classical and Quantum Dimensions, Phys. Rev. Lett. 105, 230501 (2010).

[5] J. Ahrens, P. Badziag, A. Cabello, and M. Bourennane, Experimental Device-independent Tests of Classical and Quantum Dimensions, Nature Physics 8, 592 (2012).

[6] M. Hendrych, R. Gallego, M. Mičuda, N. Brunner, A. Acín, J. P. Torres, Experimental estimation of the dimension of classical and quantum systems, Nature Physics 8, 588 (2012).

[7] M. Navascués, and T. Vértesi, Bounding the Set of Finite Dimensional Quantum Correlations, Phys. Rev. Lett. 115, 020501 (2015).

[8] M. Pawłowski, and N. Brunner, Semi-device-independent security of one-way quantum key distribution, Phys. Rev. A 84, 010302(R) (2011).

[9] H-W. Li, Z-Q. Yin, Y-C. Wu, X-B. Zou, S. Wang, W. Chen, G-C. Guo, and Z-F. Han, Semi-device-independent random-number expansion without entanglement, Phys. Rev. A 84, 034301 (2011).

[10] E. Woodhead, S. Pironio, Secrecy in Prepare-and-Measure Clauser-Horne-Shimony-Holt Tests with a Qubit Bound, Phys. Rev. Lett. 115, 150501 (2015).

[11] T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, Self-Testing Quantum Random Number Generator, Phys. Rev. Lett. 114, 150501 (2015).

[12] A. Tavakoli, J. Kaniewski, T. Vértesi, D. Rosset, and N. Brunner, Self-testing quantum states and measurements in the prepare-and-measure scenario, Phys. Rev. A 98, 062307 (2018).

[13] N. Ciganović, N. J. Beaudry, and Renato Renner, Smooth Max-Information as One-Shot Generalization for Mutual Information, IEEE Transactions on Information Theory 60, 1573 (2014).

[14] A. S. Holevo, Bounds for the quantity of information transmitted by a quantum communication channel, Problems of Information Transmission. 9, 177 (1973).

[15] R. Jozsa, D. Robb, and W. K. Wootters, Lower bound for accessible information in quantum mechanics, Phys. Rev. A 49, 668 (1994).

[16] Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, 2004.

[17] A. Ambainis, A. Nayak, A. Ta-Shma, U. Vazirani, Dense quantum coding and a lower bound for 1-way quantum automata, Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC'99), 376-383 (1999).

[18] A. Ambainis, D. Leung, L. Mancinska, M. Ozols, Quantum Random Access Codes with Shared Randomness, arXiv:0810.2937.

[19] A. Tavakoli, A. Hameedi, B. Marques, and M. Bourennane, Quantum random access codes using single d-Level systems, Phys. Rev. Lett. 114, 170502 (2015).

[20] A. Tavakoli, M. Pawłowski, M. Żukowski, and M. Bourennane, Dimensional discontinuity in quantum communication complexity at dimension seven, Phys. Rev. A 95, 020302(R) (2017).

[21] A. Tavakoli, B. Marques, M. Pawłowski, and M. Bourennane, Spatial versus sequential correlations for random access coding, Phys. Rev. A 93, 032336 (2016).

[22] A. Hameedi, D. Saha, P. Mironowicz, M. Pawłowski, and M. Bourennane, Complementarity between entanglement-assisted and quantum distributed random access code, Phys. Rev. A 95, 052345 (2017).

[23] M. Pawłowski, and M Żukowski, Entanglement-assisted random access codes, Phys. Rev. A 81, 042326 (2010).

[24] A. Tavakoli, and M. Zukowski, Higher-dimensional communication complexity problems: Classical protocols versus quantum ones based on Bell's theorem or prepare-transmit-measure schemes, Phys. Rev. A 95, 042305 (2017).

[25] N. Tishby, F. C. Pereira and W. Bialek, The information bottleneck method, Proc. of the 37th Annual Allerton Conference on Communication, Control and Computing, pages 368-377, (1999).

[26] N. Datta, C. Hirche and A. Winter, Convexity and Operational Interpretation of the Quantum Information Bottleneck Function, Proc. ISIT 2019, 7-12 July 2019, Paris, pp. 1157-1161.

[27] R. W. Spekkens, Contextuality for preparations, transformations, and unsharp measurements, Phys. Rev. A 71, 052108 (2005).

[28] R. W. Spekkens, D. H. Buzacott, A. J. Keehn, B. Toner, and G. J. Pryde, Preparation Contextuality Powers Parity-Oblivious Multiplexing, Phys. Rev. Lett. 102, 010401 (2009).

[29] A. Hameedi, A. Tavakoli, B. Marques and M. Bourennane, Communication Games Reveal Preparation Contextuality, Phys. Rev. Lett. 119, 220402 (2017).

[30] T. V. Himbeeck, E. Woodhead, N. J. Cerf, R. Garcia-Patron, and S. Pironio, Semi-device-independent framework based on natural physical assumptions, Quantum 1, 33 (2017).

[31] J. B. Brask, A. Martin, W. Esposito, R. Houlmann, J. Bowles, H. Zbinden, and N. Brunner, Megahertz-Rate Semi-Device-Independent Quantum Random Number Generators Based on Unambiguous State Discrimination, Phys. Rev. Applied 7, 054018 (2017).

[32] Y. Wang, I. W. Primaatmaja, E. Lavie, A. Varvitsiotis, C. C. W. Lim, Characterising the correlations of prepare-and-measure quantum networks, npj Quantum Information 5, 17 (2019).

[33] R. Chaves, J. B. Brask, and N. Brunner, Device-Independent Tests of Entropy, Phys. Rev. Lett. 115, 110501 (2015).

[34] M. Hayashi1, K. Iwama, H. Nishimura, R. Raymond, and S. Yamashita, (4,1)-Quantum random access coding does not exist - one qubit is not enough to recover one of four bits, New J. Phys. 8 129 (2006).

[35] A. Chailloux, I. Kerenidis, S. Kundu, and J. Sikora, Optimal bounds for parity-oblivious random access codes, New J. Phys. 18 045003 (2016).

Cited by

[1] Davide Poderini, Samuraí Brito, Ranieri Nery, Fabio Sciarrino, and Rafael Chaves, "Criteria for nonclassicality in the prepare-and-measure scenario", Physical Review Research 2 4, 043106 (2020).

[2] Anubhav Chaturvedi and Debashis Saha, "Quantum prescriptions are more ontologically distinct than they are operationally distinguishable", arXiv:1909.07293, Quantum 4, 345 (2020).

[3] Tony Metger, Yfke Dulek, Andrea Coladangelo, and Rotem Arnon-Friedman, "Device-independent quantum key distribution from computational assumptions", arXiv:2010.04175.

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