  A clock is, from an information-theoretic perspective, a system that emits
information about time. One may therefore ask whether the theory of information
imposes any constraints on the maximum precision of clocks. Here we show a
quantum-over-classical advantage for clocks or, more precisely, the task of
generating information about what time it is. The argument is based on
information-theoretic considerations: we analyse how the precision of a clock
scales with its size, measured in terms of the number of bits that could be
stored in it. We find that a quantum clock can achieve a quadratically improved
precision compared to a purely classical one of the same size.
