Feedback-Induced Advantage in Quantum Clockworks

TL;DR

This paper develops a unified theoretical framework for feedback-controlled quantum clocks, demonstrating that feedback can enhance quantum clock performance, unlike classical clocks, by improving their signal-to-noise ratio.

Contribution

It introduces a novel framework for feedback in autonomous quantum clocks and shows feedback can improve quantum clock performance, unlike classical counterparts.

Findings

Feedback preserves core features of autonomous clocks.

Classical clocks cannot surpass their optimal signal-to-noise ratio with feedback.

Quantum clocks can benefit from feedback, improving their signal-to-noise ratio.

Abstract

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 $\mathfrak{S}$ 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 performance enhancement, improving the maximal attainable signal-to-noise ratio. These results establish feedback as a potentially essential ingredient in pushing the fundamental limits of timekeeping in the quantum regime.