Optimal time for sensing in open quantum systems
Zain H. Saleem, Anil Shaji, Stephen K. Gray
Abstract
We study the time-dependent quantum Fisher information (QFI) in an open quantum system satisfying the Gorini-Kossakowski-Sudarshan-Lindblad master equation. Most of our work concerns a simple three-level model for a single probe coupled to a sink, although some results for multiple probes are also given. 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 an optimum-time-based parameter estimation procedure involving relatively low-resource-consuming measurements followed by higher-resource-consuming measurements and demonstrate it in simulation.