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.
 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).
 R. Gallego, N. Brunner, C. Hadley, and A. Acín, Device-Independent Tests of Classical and Quantum Dimensions, Phys. Rev. Lett. 105, 230501 (2010).
 J. Ahrens, P. Badziag, A. Cabello, and M. Bourennane, Experimental Device-independent Tests of Classical and Quantum Dimensions, Nature Physics 8, 592 (2012).
 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).
 M. Navascués, and T. Vértesi, Bounding the Set of Finite Dimensional Quantum Correlations, Phys. Rev. Lett. 115, 020501 (2015).
 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).
 E. Woodhead, S. Pironio, Secrecy in Prepare-and-Measure Clauser-Horne-Shimony-Holt Tests with a Qubit Bound, Phys. Rev. Lett. 115, 150501 (2015).
 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).
 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).
 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).
 A. S. Holevo, Bounds for the quantity of information transmitted by a quantum communication channel, Problems of Information Transmission. 9, 177 (1973).
 Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press, 2004.
 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).
 A. Tavakoli, A. Hameedi, B. Marques, and M. Bourennane, Quantum random access codes using single d-Level systems, Phys. Rev. Lett. 114, 170502 (2015).
 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).
 A. Tavakoli, B. Marques, M. Pawłowski, and M. Bourennane, Spatial versus sequential correlations for random access coding, Phys. Rev. A 93, 032336 (2016).
 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).
 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).
 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).
 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.
 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).
 A. Hameedi, A. Tavakoli, B. Marques and M. Bourennane, Communication Games Reveal Preparation Contextuality, Phys. Rev. Lett. 119, 220402 (2017).
 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).
 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).
 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).
 R. Chaves, J. B. Brask, and N. Brunner, Device-Independent Tests of Entropy, Phys. Rev. Lett. 115, 110501 (2015).
 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).
 A. Chailloux, I. Kerenidis, S. Kundu, and J. Sikora, Optimal bounds for parity-oblivious random access codes, New J. Phys. 18 045003 (2016).
 A. K. Pan, "Oblivious communication game, self-testing of projective and nonprojective measurements, and certification of randomness", Physical Review A 104 2, 022212 (2021).
 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).
 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).
 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).
 Armin Tavakoli, "Semi-Device-Independent Framework Based on Restricted Distrust in Prepare-and-Measure Experiments", Physical Review Letters 126 21, 210503 (2021).
 Tony Metger, Yfke Dulek, Andrea Coladangelo, and Rotem Arnon-Friedman, "Device-independent quantum key distribution from computational assumptions", arXiv:2010.04175.
The above citations are from Crossref's cited-by service (last updated successfully 2021-10-20 07:29:54) and SAO/NASA ADS (last updated successfully 2021-10-20 07:29:55). 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.