Theory-independent randomness generation from spatial symmetries

Caroline L. Jones; Stefan L. Ludescher; Albert Aloy; Markus P. Müller

doi:10.22331/q-2026-01-16-1966

Theory-independent randomness generation from spatial symmetries

Caroline L. Jones^1,2, Stefan L. Ludescher^1,2, Albert Aloy^1,2, and Markus P. Müller^1,2,3

¹Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
²Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria
³Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada

Published:	2026-01-16, volume 10, page 1966
Editor:	Leon Loveridge
Eprint:	arXiv:2210.14811v4
Doi:	https://doi.org/10.22331/q-2026-01-16-1966
Citation:	Quantum 10, 1966 (2026).

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Abstract

We demonstrate a fundamental relation between the structures of physical space and of quantum theory: the set of quantum correlations in a rotational prepare-and-measure scenario can be derived from covariance alone, without assuming quantum physics. To show this, we consider a semi-device-independent randomness generation scheme where one of two spatial rotations is performed on an otherwise uncharacterized preparation device, and one of two possible measurement outcomes is subsequently obtained. An upper bound on a theory-independent notion of spin is assumed for the transmitted physical system. It turns out that this determines the set of quantum correlations and the amount of certifiable randomness in this setup exactly. Interestingly, this yields the basis of a theory-independent protocol for the secure generation of random numbers. Our results support the conjecture that the symmetries of space and time determine at least part of the probabilistic structure of quantum theory.

Featured image: Our prepare-and-measure scenario, where the input corresponds to a spatial rotation of the preparation device.

The following is an appropriate online talk for our paper, presented alongside follow-up work:

International Symposium on Quantum Information and Communication (ISQIC), Kolkata, 31 March 2025

Popular summary

Our work explores the relationship between the symmetries of space and quantum probabilities. In particular, we explore how rotational symmetry around a fixed axis constrains the types of correlations one can expect to find in a simple “prepare-and-measure” experiment. We do so by bounding the spin of the communicated system, and compare the set of correlations as predicted by quantum theory to that of a more general, “post-quantum” set. Remarkably, we find that, for our 2-input 2-output scenario, the sets precisely coincide. That is to say, quantum physics is already the most general physical theory consistent with the symmetry of our scenario.

Our work introduces “rotation boxes” as a direct analogue to the “non-local boxes” of the famous Bell experiment. This framework gives us a way to explore the most general statistical predictions given certain minimalist assumptions, motivated by spacetime. In the case of the Bell scenario, this is the no-signalling principle (that information cannot be communicated faster than the speed of light), from which it can be shown that quantum theory is a special case. In our case, we require only that the statistical response is covariant under rotations. Under this minimal symmetry assumption, we demonstrate that the set of quantum correlations is recovered precisely for our setup.

► BibTeX data

@article{Jones2026theoryindependent,
  doi = {10.22331/q-2026-01-16-1966},
  url = {https://doi.org/10.22331/q-2026-01-16-1966},
  title = {Theory-independent randomness generation from spatial symmetries},
  author = {Jones, Caroline L. and Ludescher, Stefan L. and Aloy, Albert and M{\"{u}}ller, Markus P.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {1966},
  month = jan,
  year = {2026}
}

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[1] Caroline L. Jones, Albert Aloy, Gerard Higgins, and Markus P. Müller, "Certified Randomness From Quantum Speed Limits", PRX Quantum 7 1, 010349 (2026).

[2] Jonatan Bohr Brask, Nicolas Brunner, Jef Pauwels, Davide Rusca, and Armin Tavakoli, "Quantum correlations in prepare-and-measure scenarios and their semi-device-independent applications", arXiv:2603.23604, (2026).

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

[4] 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).

[5] Miguel Navascués, Károly F. Pál, Tamás Vértesi, and Mateus Araújo, "Self-Testing in Prepare-and-Measure Scenarios and a Robust Version of Wigner's Theorem", Physical Review Letters 131 25, 250802 (2023).

[6] Albert Aloy, Thomas D. Galley, Caroline L. Jones, Stefan L. Ludescher, and Markus P. Müller, "Spin-Bounded Correlations: Rotation Boxes Within and Beyond Quantum Theory", Communications in Mathematical Physics 405 12, 292 (2024).

[7] Lin Htoo Zaw, Mirjam Weilenmann, and Valerio Scarani, "Tsirelson's Inequality for the Precession Protocol is Maximally Violated by Quantum Theory", Physical Review Letters 134 19, 190201 (2025).

[8] Gábor Drótos, Károly F. Pál, and Tamás Vértesi, "Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario", Physical Review A 110 3, 032427 (2024).

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[10] Alireza Tavanfar, Sahar Alipour, and Ali T. Rezakhani, "Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories", Universe 11 5, 162 (2025).

[11] Gábor Drótos, Károly F. Pál, Abdelmalek Taoutioui, and Tamás Vértesi, "Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios", New Journal of Physics 26 6, 063012 (2024).

[12] Carles Roch i Carceller and Armin Tavakoli, "The role of entanglement in energy-restricted communication and randomness generation", Quantum Science and Technology 11 2, 025020 (2026).

[13] Jan Głowacki, "Operational Quantum Frames: An operational approach to quantum reference frames", arXiv:2304.07021, (2023).

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