Equation of motion for estimation fidelity of monitored oscillating qubits

We study the convergence properties of state estimates of an oscillating qubit being monitored by a sequence of discrete, unsharp measurements. Our method derives a differential equation determining the evolution of the estimation fidelity from a single incremental step. If the oscillation frequency Ω is precisely known, the estimation fidelity converges exponentially fast to unity. For imprecise knowledge of Ω we derive the asymptotic estimation fidelity.