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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[4] 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).

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

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

[7] 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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