Ticking clocks in quantum theory

TL;DR

This paper derives a general framework for quantum ticking clocks, highlighting their bipartite structure and classical information content, and introduces an information theory to distinguish their abstract and accessible information.

Contribution

It provides a unified derivation of ticking clock dynamics, clarifies their bipartite structure, and introduces an information theory for quantum clocks.

Findings

Ticking clocks have a bipartite structure with classical tick information.

The framework encompasses various existing models of quantum clocks.

An information theory distinguishes between abstract and accessible information in clocks.

Abstract

We present a derivation of the structure and dynamics of a ticking clock by showing that for finite systems a single natural principle serves to distinguish what we understand as ticking clocks from time-keeping systems in general. As a result we recover the bipartite structure of such a clock: that the information about ticks is a classical degree of freedom. We describe the most general form of the dynamics of such a clock, and discuss the additional simplifications to go from a general ticking clock to models encountered in literature. The resultant framework encompasses various recent research results despite their apparent differences. Finally, we introduce the information theory of ticking clocks, distinguishing their abstract information content and the actually accessible information.