---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20706'
abstract:
- lang: eng
  text: 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.
acknowledgement: The authors thank Georgios Katsaros for providing the device for
  this experiment, and Tony Apollaro, Ilia Khomchenko, and Gerard Milburn for discussions.
  V. W. acknowledges funding from UK Research and Innovation Grant No. EP/T517811/1.
  F. M., M. H., and P. E. acknowledge funding from the European Research Council (Consolidator
  Grant “Cocoquest” No. 101043705). M. H. and P. E. acknowledge funding from the Austrian
  Federal Ministry of Education, Science, and Research via the Austrian Research Promotion
  Agency (FFG) through Quantum Austria. R. S. acknowledges funding from the Swiss
  National Science Foundation via an Ambizione Grant No. PZ00P2_185986. M. T. M. is
  supported by a Royal Society University Research Fellowship. N. A. acknowledges
  support from the European Research Council (Grant Agreement No, 948932) and the
  Royal Society (No. URF-R1-191150). This project is cofunded by the European Union
  (Quantum Flagship project ASPECTS, Grant Agreement No. 101080167) and UK Research
  and Innovation (UKRI). Views and opinions expressed are however those of the authors
  only and do not necessarily reflect those of the European Union, Research Executive
  Agency, or UKRI. Neither the European Union nor UKRI can be held responsible for
  them.
article_number: '200407'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Vivek
  full_name: Wadhia, Vivek
  last_name: Wadhia
- first_name: Florian
  full_name: Meier, Florian
  last_name: Meier
- first_name: Federico
  full_name: Fedele, Federico
  last_name: Fedele
- first_name: Ralph
  full_name: Silva, Ralph
  last_name: Silva
- first_name: Nuriya
  full_name: Nurgalieva, Nuriya
  last_name: Nurgalieva
- first_name: David L.
  full_name: Craig, David L.
  last_name: Craig
- first_name: Daniel
  full_name: Jirovec, Daniel
  id: 4C473F58-F248-11E8-B48F-1D18A9856A87
  last_name: Jirovec
  orcid: 0000-0002-7197-4801
- first_name: Jaime
  full_name: Saez Mollejo, Jaime
  id: e0390f72-f6e0-11ea-865d-862393336714
  last_name: Saez Mollejo
- first_name: Andrea
  full_name: Ballabio, Andrea
  last_name: Ballabio
- first_name: Daniel
  full_name: Chrastina, Daniel
  last_name: Chrastina
- first_name: Giovanni
  full_name: Isella, Giovanni
  last_name: Isella
- first_name: Marcus
  full_name: Huber, Marcus
  last_name: Huber
- first_name: Mark T.
  full_name: Mitchison, Mark T.
  last_name: Mitchison
- first_name: Paul
  full_name: Erker, Paul
  last_name: Erker
- first_name: Natalia
  full_name: Ares, Natalia
  last_name: Ares
citation:
  ama: Wadhia V, Meier F, Fedele F, et al. Entropic costs of extracting classical
    ticks from a quantum clock. <i>Physical Review Letters</i>. 2025;135(20). doi:<a
    href="https://doi.org/10.1103/5rtj-djfk">10.1103/5rtj-djfk</a>
  apa: Wadhia, V., Meier, F., Fedele, F., Silva, R., Nurgalieva, N., Craig, D. L.,
    … Ares, N. (2025). Entropic costs of extracting classical ticks from a quantum
    clock. <i>Physical Review Letters</i>. American Physical Society. <a href="https://doi.org/10.1103/5rtj-djfk">https://doi.org/10.1103/5rtj-djfk</a>
  chicago: Wadhia, Vivek, Florian Meier, Federico Fedele, Ralph Silva, Nuriya Nurgalieva,
    David L. Craig, Daniel Jirovec, et al. “Entropic Costs of Extracting Classical
    Ticks from a Quantum Clock.” <i>Physical Review Letters</i>. American Physical
    Society, 2025. <a href="https://doi.org/10.1103/5rtj-djfk">https://doi.org/10.1103/5rtj-djfk</a>.
  ieee: V. Wadhia <i>et al.</i>, “Entropic costs of extracting classical ticks from
    a quantum clock,” <i>Physical Review Letters</i>, vol. 135, no. 20. American Physical
    Society, 2025.
  ista: Wadhia V, Meier F, Fedele F, Silva R, Nurgalieva N, Craig DL, Jirovec D, Saez
    Mollejo J, Ballabio A, Chrastina D, Isella G, Huber M, Mitchison MT, Erker P,
    Ares N. 2025. Entropic costs of extracting classical ticks from a quantum clock.
    Physical Review Letters. 135(20), 200407.
  mla: Wadhia, Vivek, et al. “Entropic Costs of Extracting Classical Ticks from a
    Quantum Clock.” <i>Physical Review Letters</i>, vol. 135, no. 20, 200407, American
    Physical Society, 2025, doi:<a href="https://doi.org/10.1103/5rtj-djfk">10.1103/5rtj-djfk</a>.
  short: V. Wadhia, F. Meier, F. Fedele, R. Silva, N. Nurgalieva, D.L. Craig, D. Jirovec,
    J. Saez Mollejo, A. Ballabio, D. Chrastina, G. Isella, M. Huber, M.T. Mitchison,
    P. Erker, N. Ares, Physical Review Letters 135 (2025).
date_created: 2025-11-30T23:02:07Z
date_published: 2025-11-14T00:00:00Z
date_updated: 2025-12-01T15:39:14Z
day: '14'
ddc:
- '530'
department:
- _id: GeKa
doi: 10.1103/5rtj-djfk
external_id:
  arxiv:
  - '2502.00096'
  isi:
  - '001619305100001'
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license: https://creativecommons.org/licenses/by/4.0/
month: '11'
oa: 1
oa_version: Published Version
publication: Physical Review Letters
publication_identifier:
  eissn:
  - 1079-7114
  issn:
  - 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
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status: public
title: Entropic costs of extracting classical ticks from a quantum clock
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