Fundamental Limits of Continuous Gaussian Quantum Metrology

Continuous quantum metrology holds promise for achieving high-precision sensing by harnessing information progressively carried away by radiation quanta emitted into the environment. Despite recent progress, a comprehensive understanding of the fundamental precision limits of continuous metrology with bosonic systems is still lacking. In this work, we develop a theoretical framework for quantum metrology in free-bosonic systems under continuous Gaussian measurements. We derive analytical expressions for the asymptotic growth rates of the global quantum Fisher information (QFI) and the environmental QFI, which quantify the total information encoded in the joint system-environment state and the information accessible from the emitted radiation, respectively. We further establish fundamental bounds on these quantities in terms of available resources, namely the number of bosonic modes and the bosonic excitation number. Finally, we analyze several concrete scenarios to illustrate our framework.