  Quantum properties of the probes used to estimate a classical parameter can
be used to attain accuracies that beat the standard quantum limit. When qubits
are used to construct a quantum probe, it is known that initializing $n$ qubits
in an entangled "cat state," rather than in a separable state, can improve the
measurement uncertainty by a factor of $1/\sqrt{n}$. We investigate how the
measurement uncertainty is affected when the individual qubits in a probe are
subjected to decoherence. In the face of such decoherence, we regard the rate
$R$ at which qubits can be generated and the total duration $\tau$ of a
measurement as fixed resources, and we determine the optimal use of
entanglement among the qubits and the resulting optimal measurement uncertainty
as functions of $R$ and $\tau$.
