An information theory for clocks and synchronisation

To establish operational reference frames for time, one requires physical clocks that periodically send signals to observers. The synchronisation between the various signals determines the quality of the time reference.

In this talk I will discuss the information theory of this synchronisation. By viewing the sequence of signals marked by their emitting clock as a random process, one can define a natural measure of information based on the distance to the random process generated by `trivial' clocks. We show that the measure bounds existing measures of the precision of clocks, for both discrete and continuous signals. Finally we discuss how quantum clocks can be cast as a Hidden Markov Model. The aim of this work is to lay the groundwork for establishing fundamental relations between the physical properties of clocks (mass, size, etc.) and the information content of their synchronised signals.