Qubit metrology and decoherence

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 state, rather than in a separable state, can improve the measurement uncertainty by a factor of 1/root 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.