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  • Featured in Physics
  • Open Access

Autonomous Quantum Clocks: Does Thermodynamics Limit Our Ability to Measure Time?

Paul Erker1,2, Mark T. Mitchison3,4, Ralph Silva5, Mischa P. Woods6,7, Nicolas Brunner5, and Marcus Huber8

  • 1Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
  • 2Faculty of Informatics, Università della Svizzera italiana, Via G. Buffi 13, 6900 Lugano, Switzerland
  • 3Quantum Optics and Laser Science Group, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom
  • 4Institut für Theoretische Physik, Albert-Einstein Allee 11, Universität Ulm, 89069 Ulm, Germany
  • 5Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
  • 6University College London, Department of Physics & Astronomy, London WC1E 6BT, United Kingdom
  • 7QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft, Netherlands
  • 8Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, A-1090 Vienna, Austria

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Phys. Rev. X 7, 031022 – Published 2 August, 2017

DOI: https://doi.org/10.1103/PhysRevX.7.031022

Abstract

Time remains one of the least well-understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly. Here, we explore these questions by introducing a model of time measurements that is complete and autonomous. Specifically, our autonomous quantum clock consists of a system out of thermal equilibrium—a prerequisite for any system to function as a clock—powered by minimal resources, namely, two thermal baths at different temperatures. Through a detailed analysis of this specific clock model, we find that the laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock’s performance in terms of its accuracy and resolution. Our results furthermore imply that a fundamental entropy production is associated with the operation of any autonomous quantum clock, assuming that quantum machines cannot achieve perfect efficiency at finite power. More generally, autonomous clocks provide a natural framework for the exploration of fundamental questions about time in quantum theory and beyond.

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Physics Subject Headings (PhySH)

Viewpoint

The Thermodynamic Cost of Measuring Time

Published 2 August, 2017

A simple model of an autonomous quantum clock yields a quantitative connection between the clock’s thermodynamic cost and its accuracy and resolution.

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Popular Summary

Time is arguably one of the most prominent concepts in physics, yet it still holds a significant number of mysteries, particularly in the context of quantum physics. Quantum theory fails to provide a clear description of what time actually is and treats it simply as a classical external variable. It is often argued that this failure represents one of the obstacles to unifying quantum theory with general relativity. Here, we theoretically explore the ultimate limitation of measuring time based only on the laws of quantum physics.

We introduce the concept of an autonomous quantum clock, which represents a minimal model of a quantum clock that is both complete and self-contained. It allows us to elucidate the fundamental limitations in the process of timekeeping without implicitly assuming unaccounted-for resources through external control. We consider that our out-of-thermal-equilibrium clock is powered by two thermal baths held at different temperatures. We show that the clock’s accuracy and resolution—its performance—are intimately related to the power the clock dissipates. In other words, measuring time results in an increase in entropy. This finding provides a quantitative basis for the intuitive connection between the second law of thermodynamics and the arrow of time.

We expect that the concepts and tools we have developed will enable other researchers to explore novel questions about time in quantum theory and beyond.

Article Text

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Phys. Rev. X 7, 031022– Published 2 August, 2017
  • Received 7 November 2016
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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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