Nonclassical Temporal Correlations Enhance the Performance of Ticking Clocks

Abstract

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. Moreover, the idea of ticking clocks inspires the derivation of a new family of temporal inequalities showing a gap between classical and quantum correlations. We present analytical and numerical results showing that quantum ticking-clock models achieving accuracy beyond the classical bound are also those violating Leggett-Garg-type temporal inequalities for finite sequences. We also investigate the continuous limit of our models and its relation with known results in the literature.