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Quantum Stroboscopy for Time Measurements

Seth Lloyd1, Lorenzo Maccone2, Lionel Martellini3, and Simone Roncallo2

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Phys. Rev. Lett. 136, 110201 – Published 20 March, 2026

DOI: https://doi.org/10.1103/58vf-m1yx

Abstract

Mielnik’s cannonball argument uses the Zeno effect to argue that projective measurements for time of arrival are impossible. If one repeatedly measures the position of a particle (or a cannonball!) that has yet to arrive at a detector, the Zeno effect will repeatedly collapse its wave function away from it: the particle never arrives. Here we introduce quantum stroboscopic measurements where we accumulate statistics of projective position measurements, performed on different copies of the system at different times, to obtain a time-of-arrival distribution. We show that, under appropriate limits, this gives the same statistics as time measurements of conventional “always on” particle detectors that bypass Mielnik’s argument using nonprojective, weak continuous measurements. In addition to time of arrival, quantum stroboscopy can describe distributions of general time measurements. It can also be adapted to obtain the conditional probability distribution of arrival times, given that the particle was not previously detected at the detector.

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Phys. Rev. Lett. 136, 110201– Published 20 March, 2026
  • Received 1 October 2025
  • Revised 23 December 2025
  • Accepted 20 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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