  A quantum clock must satisfy two basic constraints. The first is a bound on
the time resolution of the clock given by the difference between its maximum
and minimum energy eigenvalues. The second follows from Holevo's bound on how
much classical information can be encoded in a quantum system. We show that
asymptotically, as the dimension of the Hilbert space of the clock tends to
infinity, both constraints can be satisfied simultaneously. The experimental
realization of such an optimal quantum clock using trapped ions is discussed.
