Hi all,
Tomorrow Kai Ott will tell us about his semester project with Mischa Woods and Joe Renes, entitled 'Understanding Quantum Clocks: Measures of Precision and Entropy Production'. See below for the abstract. The talk will take place at 2pm in HIT F 32 or on Zoom: https://ethz.zoom.us/j/362994444.
Best, Ladina
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Recent work on quantum clocks has shown quantum-over-classical advantage in time-keeping. In particular, in the limit of large dimensions, quantum ticking clocks can achieve arbitrary precision $R_1$ at vanishing entropy production $\Sigma_1$ per tick, while for classical clocks there is a fundamental trade-off between precision and entropy production per tick, i.e. for any desired precision, there is an associated minimal entropy production. In this work, we show that another type of precision $I_1$ defined via the relative entropy can be made arbitrarily large at vanishing entropy production even for classical ticking clocks of finite dimension. Then, we investigate optimal classical clocks, which achieve the minimum entropy production per tick for a given precision $R_1$. We give closed form solutions for their precision, discuss symmetries, and state how their parameters should be chosen to truly be optimal. Lastly, we relate the classical case to the quantum case to explain the approximate quadratic precision advantage of the latter over the former.