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arXiv:2005.04628 · Quantum

Autonomous Ticking Clocks from Axiomatic Principles

Mischa P. Woods

Published Jan 17, 2021• 19 citations
arXivHTMLPDF

Abstract

There are many different types of time keeping devices. We use the phrase ticking clock to describe those which – simply put – ``tick'' at approximately regular intervals. Various important results have been derived for ticking clocks, and more are in the pipeline. It is thus important to understand the underlying models on which these results are founded. The aim of this paper is to introduce a new ticking clock model from axiomatic principles that overcomes concerns in the community about the physicality of the assumptions made in previous models. The ticking clock model in \cite{woods2018quantum} achieves high accuracy, yet lacks the autonomy of the less accurate model in \cite{thermoClockErker}. Importantly, the model we introduce here achieves the best of both models: it retains the autonomy of \cite{thermoClockErker} while allowing for the high accuracies of \cite{woods2018quantum}. What is more, \cite{thermoClockErker} is revealed to be a special case of the new ticking clock model.

DOI
10.22331/q-2021-01-17-381

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Comment on "Entropic Costs of Extracting Classical Ticks from a Quantum Clock"

Longyan Gong

A recent Letter by Wadhia et al. reports a realization of a quantum clock using a double quantum dot (DQD) [Phys. Rev. Lett. 135, 200407 (2005)]. This Comment identifies two fundamental issues: (I) the claimed ``quantum clock" exhibits only classical behavior and lacks intrinsic temporal correlations between ticks; it is not sufficient for accurate time as a good clock. (II) the thermodynamic analysis misassigns entropy production and conflates amplification with measurement; the reported combined entropy is an engineering dissipation, not a fundamental cost of quantum timekeeping.

cond-mat.mes-hallCross-listedarXiv:2605.21833•May 22, 2026•0 citations
There are many different types of time keeping devices. We use the phrase ticking clock to describe those which – simply put – ``tick'' at approximately regular intervals. Various important results have been derived for ticking clocks, and more are in the pipeline. It is thus important to understand the underlying models on which these results are founded. The aim of this paper is to introduce a new ticking clock model from axiomatic principles that overcomes concerns in the community about the physicality of the assumptions made in previous models. The ticking clock model in \cite{woods2018quantum} achieves high accuracy, yet lacks the autonomy of the less accurate model in \cite{thermoClockErker}. Importantly, the model we introduce here achieves the best of both models: it retains the autonomy of \cite{thermoClockErker} while allowing for the high accuracies of \cite{woods2018quantum}. What is more, \cite{thermoClockErker} is revealed to be a special case of the new ticking clock model.
We present a derivation of the structure and dynamics of a ticking clock by showing that for finite systems a single natural principle serves to distinguish what we understand as ticking clocks from time-keeping systems in general. As a result we recover the bipartite structure of such a clock: that the information about ticks is a classical degree of freedom. We describe the most general form of the dynamics of such a clock, and discuss the additional simplifications to go from a general ticking clock to models encountered in literature. The resultant framework encompasses various recent research results despite their apparent differences. Finally, we introduce the information theory of ticking clocks, distinguishing their abstract information content and the actually accessible information.
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.
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.
Here we explore the possibility of precise time keeping in quantum systems using athermal resources. We show that quantum measurement engineered reservoirs can be used as athermal resources to drive the ticks of a quantum clock. Two- and three-level quantum systems act as transducers in our model, converting the quantum measurement-induced noise to produce a series of ticks. The ticking rate of the clock is maximized when the measured observable maximally noncommutes with the clock's Hamiltonian. We use the large deviation principle to characterize the statistics of observed ticks within a given time period and show that it can be sub-Poissonian---quantified by Mandel's Q parameter---alluding to the quantum nature of the clock. We discuss the accuracy and efficiency of the clock, and extend our framework to include hybrid quantum clocks fueled by both measurements, and thermal resources. We make comparisons to relatable recent proposals for quantum clocks, and discuss alternate device implementations harvesting the quantum measurement engineered nonequilibrium conditions, beyond the clock realization.
We investigate the role of nonclassical temporal correlations in enhancing the performance of ticking clocks in a discrete-time scenario. We show that the problem of optimal models for ticking clocks is related to the violation of Leggett-Garg-type temporal inequalities formulated in terms of, possibly invasive, sequential measurements, but on a system with a bounded memory capacity. Ticking clocks inspire the derivation of a family of temporal inequalities showing a gap between classical and quantum correlations, despite involving no input. We show that quantum ticking-clock models achieving accuracy beyond the classical bound are also those violating Leggett-Garg-type temporal inequalities for finite sequences and we investigate their continuous-time limit. Interestingly, we show that optimal classical clock models in the discrete-time scenario do not have a well-defined continuous-time limit, a feature that is absent in quantum models.
A recent Letter by Wadhia et al. reports a realization of a quantum clock using a double quantum dot (DQD) [Phys. Rev. Lett. 135, 200407 (2005)]. This Comment identifies two fundamental issues: (I) the claimed ``quantum clock" exhibits only classical behavior and lacks intrinsic temporal correlations between ticks; it is not sufficient for accurate time as a good clock. (II) the thermodynamic analysis misassigns entropy production and conflates amplification with measurement; the reported combined entropy is an engineering dissipation, not a fundamental cost of quantum timekeeping.