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  • Open Access

Certified Randomness From Quantum Speed Limits

Caroline L. Jones1,2,*,†, Albert Aloy1,2,†,‡, Gerard Higgins1,3, and Markus P. Müller1,2,4

  • *Contact author: CarolineLouise.Jones@oeaw.ac.at
  • †These authors contributed equally to this work.
  • ‡Contact author: Albert.Aloy@oeaw.ac.at
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PRX Quantum 7, 010349 – Published 11 March, 2026

DOI: https://doi.org/10.1103/bnrq-sp5w

Abstract

Quantum speed limits are usually regarded as fundamental restrictions, constraining the amount of computation that can be achieved within some given time and energy. Complementary to this intuition, here we show that these limitations are also of operational value: they enable the secure generation of certified randomness. We consider a prepare-and-measure scenario with some (experimentally determined or promised) upper bound on the energy uncertainty ΔE of the average prepared quantum state, but without any further assumptions on the devices, Hilbert space or Hamiltonian. Given that we can freely choose the time at which to apply the untrusted preparation procedure, we show that this scenario admits the generation of randomness that is secure against adversaries with additional classical information. We show how to determine the amount of certified randomness given the observed correlations, discuss how interactions with the environment are taken into account, and sketch a conceivable experimental implementation. In particular, we show that single-mode coherent states admit this kind of certification of nonzero randomness in some parameter regimes, reinforcing existing demonstrations of nonclassicality in the simple harmonic oscillator. Our results extend earlier efforts to devise semi-device-independent protocols grounded in reasonable physical assumptions, and they contribute to the understanding of time-energy uncertainty relations via their operational consequences.

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Popular Summary

Quantum speed limits (QSLs) are fundamental restrictions on how quickly a quantum system can evolve. They tell us, for example, that computers cannot run arbitrarily fast unless they contain an unbounded amount of energy, and are therefore commonly viewed as obstacles in quantum information processing. Contrary to this intuition, we show that QSLs can also be a valuable tool—specifically, as a mechanism for the generation of secure randomness.

Certifiably random numbers are an important resource in quantum technologies. Whilst quantum theory predicts that many outcomes of experiments are random, applications in cryptography require a much more paranoid result: numbers that not only look random, but that are provably unpredictable—even by eavesdroppers who know more about our lab devices than we do. We contribute to a long-standing line of research regarding how this can be accomplished; by bounding the energy uncertainty of a quantum system, the time-energy QSL can be harnessed for randomness generation.

More broadly, our work explores the interplay between quantum information and spacetime symmetries, by putting the traditionally abstract black boxes of quantum information into space and time. Beyond opening new possibilities for physically grounded protocols, our work contributes to our understanding of QSLs as tools for witnessing nonclassicality by analyzing their operational consequences.

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PRX Quantum 7, 010349– Published 11 March, 2026
  • Received 9 July 2025
  • Accepted 6 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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