Equation of Motion for Estimation Fidelity of Monitored Oscillating Qubits
arXiv:1705.10348 · doi:10.1016/j.physleta.2017.05.013
Abstract
We study the convergence properties of state estimates of an oscillating qubit being monitored by a sequence of \textit{discrete}, unsharp measurements. Our method derives a differential equation determining the evolution of the estimation fidelity from a single incremental step. When the oscillation frequency $Ω$ is precisely known, the estimation fidelity converges exponentially fast to unity. For imprecise knowledge of $Ω$ we derive the asypmtotic estimation fidelity.
5 pages, 3 figures