Bayesian quantum frequency estimation in presence of collective dephasing

We advocate a Bayesian approach to optimal quantum frequency estimation-an important issue for future quantum enhanced atomic clock operation. The approach provides a clear insight into the interplay between decoherence and the extent of prior knowledge in determining the optimal interrogation times and optimal estimation strategies. We propose a general framework capable of describing local oscillator noise as well as additional collective atomic dephasing effects. For a Gaussian noise, the average Bayesian cost can be expressed using the quantum Fisher information. Thus we establish a direct link between the two, often competing, approaches to quantum estimation theory.