Optimal time for sensing in open quantum systems

TL;DR

This paper investigates the optimal timing for quantum parameter estimation in open quantum systems by analyzing quantum Fisher information dynamics, proposing a practical measurement strategy, and exploring non-Hermitian perspectives.

Contribution

It introduces a method to identify optimal measurement times for maximum QFI and proposes a resource-efficient estimation procedure in open quantum systems.

Findings

QFI peaks at specific times, indicating optimal measurement points.

The proposed measurement strategy improves estimation precision with fewer resources.

Non-Hermitian dynamics provide insights into QFI scaling with multiple probes.

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.