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

Armin Tavakoli; Emmanuel Zambrini Cruzeiro; Erik Woodhead; Stefano Pironio

doi:10.22331/q-2022-01-05-620

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

Armin Tavakoli^1,2, 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

Published:	2022-01-05, volume 6, page 620
Eprint:	arXiv:2007.16145v4
Doi:	https://doi.org/10.22331/q-2022-01-05-620
Citation:	Quantum 6, 620 (2022).

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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

@article{Tavakoli2022informationally,
  doi = {10.22331/q-2022-01-05-620},
  url = {https://doi.org/10.22331/q-2022-01-05-620},
  title = {Informationally restricted correlations: a general framework for classical and quantum systems},
  author = {Tavakoli, Armin and Zambrini Cruzeiro, Emmanuel and Woodhead, Erik and Pironio, Stefano},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {620},
  month = jan,
  year = {2022}
}

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[2] Piotr Mironowicz, "Semi-definite programming and quantum information", Journal of Physics A: Mathematical and Theoretical 57 16, 163002 (2024).

[3] Mário Silva, Ricardo Faleiro, Paulo Mateus, and Emmanuel Zambrini Cruzeiro, "A coherence-witnessing game and applications to semi-device-independent quantum key distribution", Quantum 7, 1090 (2023).

[4] Moisés Alves, Vitor L. Sena, Santiago Zamora, Tailan S. Sarubi, A. de Oliveira Junior, Alexandre B. Tacla, and Rafael Chaves, "Semi-device-independent randomness certification on discretized continuous-variable platforms", Physical Review A 113 4, 042418 (2026).

[5] Elna Svegborn, Jef Pauwels, and Armin Tavakoli, "Quantum inputs in the prepare-and-measure scenario and stochastic teleportation", Quantum Science and Technology 11 2, 025001 (2026).

[6] Carles Roch i Carceller, Jef Pauwels, Stefano Pironio, and Armin Tavakoli, "Prepare-and-Measure Scenarios with Photon-Number Constraints", Physical Review Letters 135 14, 140802 (2025).

[7] Carlos Vieira, Carlos de Gois, Lucas Pollyceno, and Rafael Rabelo, "Interplays between classical and quantum entanglement-assisted communication scenarios", New Journal of Physics 25 11, 113004 (2023).

[8] Lorenzo Catani, Ricardo Faleiro, Pierre-Emmanuel Emeriau, Shane Mansfield, and Anna Pappa, "Connecting xor and xor * games", Physical Review A 109 1, 012427 (2024).

[9] Alexander Bernal, Gabriele Cobucci, Martin J. Renner, and Armin Tavakoli, "Absolute Dimensionality of Quantum Ensembles", Physical Review Letters 133 24, 240203 (2024).

[10] Rafael Wagner, Filipa C R Peres, Emmanuel Zambrini Cruzeiro, and Ernesto F Galvão, "Unitary-invariant method for witnessing nonstabilizerness in quantum processors", Journal of Physics A: Mathematical and Theoretical 58 28, 285302 (2025).

[11] Jef Pauwels, Armin Tavakoli, Erik Woodhead, and Stefano Pironio, "Entanglement in prepare-and-measure scenarios: many questions, a few answers", New Journal of Physics 24 6, 063015 (2022).

[12] Ankush Pandit, Soumyabrata Hazra, Satyaki Manna, Anubhav Chaturvedi, and Debashis Saha, "Limits of classical correlations and quantum advantages under (anti-)distinguishability constraints in multipartite communication", Physical Review A 113 3, 032433 (2026).

[13] Simon Morelli, Hayata Yamasaki, Marcus Huber, and Armin Tavakoli, "Entanglement Detection with Imprecise Measurements", Physical Review Letters 128 25, 250501 (2022).

[14] Caroline L. Jones, Stefan L. Ludescher, Albert Aloy, and Markus P. Müller, "Theory-independent randomness generation from spatial symmetries", Quantum 10, 1966 (2026).

[15] Jef Pauwels, Stefano Pironio, Erik Woodhead, and Armin Tavakoli, "Almost Qudits in the Prepare-and-Measure Scenario", Physical Review Letters 129 25, 250504 (2022).

[16] Jef Pauwels, Stefano Pironio, and Armin Tavakoli, "Information capacity of quantum communication under natural physical assumptions", Quantum 9, 1637 (2025).

[17] Satyaki Manna, Anubhav Chaturvedi, and Debashis Saha, "Unbounded quantum advantage in communication complexity measured by distinguishability", Physical Review Research 6 4, 043269 (2024).

[18] Meng-Yun Ma, Kai-Mei Zheng, Xu Xu, Chao-Jie Sun, Qi-Ping Su, Chui-Ping Yang, and Yong-Nan Sun, "Experimental investigation of quantum correlations under restricted distrust in a semi-device-independent framework", Optics Express 32 24, 43703 (2024).

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[22] Armin Tavakoli, Alejandro Pozas-Kerstjens, Peter Brown, and Mateus Araújo, "Semidefinite programming relaxations for quantum correlations", Reviews of Modern Physics 96 4, 045006 (2024).

[23] Armin Tavakoli, Alejandro Pozas-Kerstjens, Ming-Xing Luo, and Marc-Olivier Renou, "Bell nonlocality in networks", Reports on Progress in Physics 85 5, 056001 (2022).

[24] Rahul Jain and Srijita Kundu, "A Direct Product Theorem for Quantum Communication Complexity with Applications to Device-Independent Cryptography", SIAM Journal on Computing 54 4, 964 (2025).

[25] 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).

[26] 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).

[27] Caroline L. Jones, Stefan L. Ludescher, Albert Aloy, and Markus P. Mueller, "Theory-independent randomness generation from spatial symmetries", arXiv:2210.14811, (2022).

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

[29] Rafael Wagner, "Coherence and contextuality as quantum resources", arXiv:2511.16785, (2025).

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

[31] 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).

[32] Ming-Xing Luo, "Network configuration theory for all networks", arXiv:2107.05846, (2021).

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