Optimal time for sensing in open quantum systems

Abstract: We study the time-dependent quantum Fisher information (QFI) in an open quantum system satisfying the Gorini-Kossakowski-Sudarshan-Lindblad master equation. We also study the dynamics of the system from an effective non-Hermitian dynamics standpoint and use it to understand the scaling of the QFI when multiple probes are used. A focus of our work is how the QFI is maximized at certain times suggesting that the best precision in parameter estimation can be achieved by focusing on these times. The propagation of errors analysis allows us to confirm and better understand this idea. We also propose a parameter estimation procedure involving relatively low resource consuming measurements followed by higher resource consuming measurements and demonstrate it in simulation.