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. 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.
Highlights
The long-standing problem of understanding time in quantum theory has recently acquired renewed interest from the perspective of an operational definition of time and the practical and fundamental limitations to its measurement or even its definition [1,2,3,4,5,6,7]
We investigate the role of nonclassical temporal correlations in enhancing the performance of ticking clocks in a discrete-time scenario
We show that optimal classical clock models in the discrete-time scenario do not have a well-defined continuoustime limit, a feature that is absent in quantum models
Summary
The long-standing problem of understanding time in quantum theory has recently acquired renewed interest from the perspective of an operational definition of time and the practical and fundamental limitations to its measurement or even its definition [1,2,3,4,5,6,7]. Due to an imperfect, or clumsy, measurement rather than quantum effects This strong restriction on allowed operations makes it difficult to discuss in terms of Leggett-Garg inequalities quantum advantages in information-theoretic tasks involving sequential operations: Any classical device with an internal memory that is updated sequentially would violate NIM. We first show how the notion of the accuracy of a ticking clock gives rise to a family of temporal inequalities and prove analytically the bound for the bit case Such inequalities, involving first and second moments of the ticks’ distribution, need infinitely long sequences. Optimal classical clocks do not always have a well-defined continuous limit, in contrast with quantum clocks, which are readily extended to the continuous-time limit in all cases
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