Optimal quantum clocks

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 maxim um and minimum energy eigenvalues. The second follows from Holevo's bound o n how much classical information can be encoded in a quantum system. We sho w that asymptotically, as the dimension of the Hilbert space of the clock t ends to infinity, both constraints can be satisfied simultaneously. The exp erimental realization of such an optimal quantum clock using trapped ions i s discussed.