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arXiv:2609.31837

Measuring Clock Precision Without an Ideal Time Reference

Pablo Á. Domínguez, Christopher Chubb, Mischa P. Woods

quant-phSubmitted Sep 25, 2026• Announced Sep 29, 2026• 0 citations
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Abstract

Characterising physical devices typically requires comparison with more precise reference standards. For clocks, however, this approach is problematic because no physically perfect time reference exists; real clocks have finite, model-dependent uncertainty. We address whether multiple imperfect clocks can collectively determine their precision without an absolute reference. This paper provides analytic bounds and protocols for quantifying clock precision using only multiple copies of the same clock, which need not be synchronised and may have manufacturing variations or environmental coupling. Beyond clock characterisation, these methods enable precise measurements f sub-period intervals and relativistic effects such as time dilation and Doppler shifts, providing tools for quantum metrology and fundamental physics.

Comments
19 pages, 4 figures

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Characterising physical devices typically requires comparison with more precise reference standards. For clocks, however, this approach is problematic because no physically perfect time reference exists; real clocks have finite, model-dependent uncertainty. We address whether multiple imperfect clocks can collectively determine their precision without an absolute reference. This paper provides analytic bounds and protocols for quantifying clock precision using only multiple copies of the same clock, which need not be synchronised and may have manufacturing variations or environmental coupling. Beyond clock characterisation, these methods enable precise measurements f sub-period intervals and relativistic effects such as time dilation and Doppler shifts, providing tools for quantum metrology and fundamental physics.
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Precise time synchronisation underpins critical infrastructure from telecommunications and financial markets to power grids and scientific metrology. Several families of quantum protocols have been proposed and demonstrated for clock synchronisation and time distribution, exploiting entangled photon pairs, quantum key distribution (QKD) correlations, Hong-Ou-Mandel interference, and entangled clock networks. We critically assess these approaches, reviewing the main quantum time synchronisation (QTS) protocol families, quantifying the gap between theory and experiment, and identifying practical bottlenecks in sources, detectors, and channels. We survey the classical timing landscape from Network Time Protocol (NTP) and GPS to laboratory-grade optical frequency transfer, and compare quantum and classical methods at equivalent maturity. We examine use cases including financial trading, power grids, telecommunications, scientific metrology, and military applications, evaluating whether quantum timing offers a realistic advantage. We show that time transfer, not clock performance, is now the bottleneck for distributed optical timekeeping: the best demonstrated synchronisation uncertainty (2.46~ps) falls two to three orders of magnitude short of what optical clocks with fractional frequency uncertainties of 10−1810^{-18}10−18--10−1910^{-19}10−19 require. Our assessment is that quantum time synchronisation will not replace classical methods for most applications in the near-to-medium future. Its near-term value lies in physical-layer security against timing manipulation and integration with quantum communication networks, while closing the synchronisation gap for scientific metrology remains the most critical open challenge.
Precision metrology has undergone a revolution thanks to quantum measurement techniques, which have made it possible to determine basic constants with previously unheard-of accuracy and to improve timekeeping. These techniques, which are based on the ideas of quantum physics, use entanglement, superposition, and quantum state interference to increase measurement accuracy beyond what is possible with classical approaches. the most recent advancements in high-precision quantum measurement methods, with an emphasis on how they can be used to determine fundamental constants like Planck's constant and the fine-structure constant. Additionally, atomic clocks and optical lattice clocks have advanced timekeeping by providing remarkably accurate time standards. There is also discussion of how quantum-enhanced sensors can improve temperature, electromagnetic field, and gravitational wave measurements. In order to redefine precision in science and industry, we conclude by outlining potential directions for incorporating quantum technologies into global metrology frameworks.
The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all ``good'' quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures – a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.
The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all ``good'' quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures – a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.