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Entropic Costs of Extracting Classical Ticks from a Quantum Clock

Vivek Wadhia1,*,†, Florian Meier2,*,‡, Federico Fedele1, Ralph Silva3, Nuriya Nurgalieva4, David L. Craig5, Daniel Jirovec6, Jaime Saez-Mollejo6, Andrea Ballabio7 et al.

Daniel Chrastina7, Giovanni Isella7, Marcus Huber2,8, Mark T. Mitchison9,10, Paul Erker2,8, and Natalia Ares1,§

  • *These authors contributed equally to this work.
  • †Contact author: vivek.wadhia@eng.ox.ac.uk
  • ‡Contact author: florianmeier256@gmail.com
  • §Contact author: natalia.ares@eng.ox.ac.uk
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Phys. Rev. Lett. 135, 200407 – Published 14 November, 2025

DOI: https://doi.org/10.1103/5rtj-djfk

Abstract

We experimentally realize a quantum clock by using a charge sensor to count charges tunneling through a double quantum dot (DQD). Individual tunneling events are used as the clock’s ticks. We quantify the clock’s precision while measuring the power dissipated by the DQD and, separately, the charge sensor in both direct-current and radio-frequency readout modes. This allows us to probe the thermodynamic cost of creating ticks microscopically and recording them macroscopically. Our experiment is the first to explore the interplay between the entropy produced by a microscopic clockwork and its macroscopic measurement apparatus. We show that the latter contribution not only dwarfs the former but also unlocks greatly increased precision, because the measurement record can be exploited to optimally estimate time even when the DQD is at equilibrium. Our results suggest that the entropy produced by the amplification and measurement of a clock’s ticks, which has often been ignored in the literature, is the most important and fundamental thermodynamic cost of timekeeping at the quantum scale.

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The Costs of Quantum Timekeeping

Published 14 November, 2025

Experiments reveal the surprisingly large amount of entropy—and thus heat—generated by a clock that could be part of a quantum processor.

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Outline

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Phys. Rev. Lett. 135, 200407– Published 14 November, 2025
  • Received 3 March 2025
  • Revised 4 July 2025
  • Accepted 16 September 2025
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