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arXiv:2609.31832

Characterising the precision of a clock without any external time reference

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

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

Determining a clock's precision usually requires comparison with a better time reference, yet no ideal reference is physically attainable. We show how a single clock can characterise its own precision using only a signal splitter and delayed trigger, whose uncertainty is explicitly accounted for. The resulting estimator depends only on tick-count statistics. A purpose-built electronic circuit validates the method without an external timekeeper or a second clock.

Comments
8 pages, 4 figures

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Determining a clock's precision usually requires comparison with a better time reference, yet no ideal reference is physically attainable. We show how a single clock can characterise its own precision using only a signal splitter and delayed trigger, whose uncertainty is explicitly accounted for. The resulting estimator depends only on tick-count statistics. A purpose-built electronic circuit validates the method without an external timekeeper or a second clock.
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.
It is a key principle of quantum mechanics that plane matter waves are proportional to exp(-ipμxμ/ℏ)=exp(-iω0τ), where pμand xμare respectively 4-momentum and position, and τ is the proper time measured along the particle's tra-jectory. Thus, the quantum state of a free particle of mass m accumulates the same phase as a clock ticking at the particle's Compton frequency of ω0=mc2/ℏ travelling along the particle's trajectory. This equality, if it is not just an artifact of the theory, implies that a single particle can be a reference for a clock. In principle, such a clock could be built by annihilating particle-antiparticle pairs and counting the frequencies of the generated photons. This would provide a frequency reference with virtually infinite quality factor Q and unsurpassed stability against systematic influences. The frequency (ω0/2π=3×1025Hz for a Cesium atom), however, is far beyond modern counting techniques. A method to divide it into a technically accessible range is thus required.
Creating precise timing devices at ultra-short time scales is not just an important technological challenge, but confronts us with foundational questions about timekeeping's ultimate precision limits. Research on clocks has either focused on long-term stability using an oscillator stabilized by a level transition, limiting precision at short timescales, or on making individual stochastic ticks as precise as possible. Here, we prove the viability of a conceptually different avenue: the autonomous self-correction of consecutive ticks by quantum correlations. This provides a new paradigm that integrates the advantages and insights from quantum transport theory to operate clocks at ultra-short timescales. We fully solve a model of coupled quantum systems and show how the emergent Pauli exclusion principle correlates the clock at the quantum level yielding an exponential advantage in precision. We furthermore demonstrate through simulations with realistic imperfections that this remarkable gain in precision remains stable providing a roadmap for implementation with contemporary quantum technologies.
We show that finite physical clocks always have well-behaved signals, namely that every waiting-time distribution generated by a physical process on a system of finite size is guaranteed to be bounded by a decay envelope. Following this consideration, we show that one can reconstruct the distribution using only operationally available information, namely, that of the ordering of the ticks of one clock with the respect to those of another clock (which we call the reference), and that the simplest possible reference clock -- a Poisson process -- suffices.
Atomic frequency standards have achieved steadily increasing precision over the past seventy years, enabled in part by feedback mechanisms that stabilise their output. In parallel, the timekeeping capabilities of quantum systems have been explored within the recently developed ticking-clock framework, which models clocks as dynamical systems producing a stochastic sequence of ticks. However, a theoretical description that unifies these perspectives and incorporates feedback into autonomous quantum clocks has been lacking. We introduce a framework for feedback-controlled clockworks in which classical information extracted from the tick sequence is used to influence the subsequent dynamics of the clock. We show that such feedback preserves the core structural features of self-timing and clockwork independence that characterise autonomous ticking clocks. We further identify the signal-to-noise ratio S\mathfrak{S}S as the fundamental figure of merit for assessing the performance of feedback-controlled clocks. Applying our framework to two representative architectures, we prove that classical clockworks cannot surpass the optimal signal-to-noise ratio achievable without feedback. In contrast, for quantum clockworks we present numerical evidence that feedback can provide a genuine and robust performance enhancement, improving the maximal attainable signal-to-noise ratio. We provide additional numerical evidence, suggesting that the magnitude of the improvement strongly depends on the amount and type of the stored, classical information. These results establish feedback as a potentially essential ingredient in pushing the fundamental limits of timekeeping in the quantum regime.