Quantum metrology of a structured reservoir

Abstract: Accurately characterizing the properties of structured reservoirs is a key challenge in quantum systems and is of great importance for advances in quantum metrology and sensing. In this work, we employ a two-level system (qubit) as a probe, which is coupled to a structured reservoir consisting of an ancilla qubit and a Markovian environment modeled as a thermal bath. By exploiting non-Markovian dynamics, we systematically investigate the effectiveness of different interaction types between the probe and ancilla for estimating critical parameters, including temperature, ancilla frequency, and system-bath coupling strength. We quantify the precision of parameter estimation using quantum Fisher information (QFI) and analyze the system dynamics in both transient and steady-state regimes. Our findings demonstrate that non-Markovianity substantially enhances parameter estimation in the transient regime, with specific interactions facilitating sustained information backflow and yielding higher QFI values. However, the performance of these interactions is contingent on the parameter under estimation and the operational regime. For instance, certain interactions become prominent in the transient regime but exhibit diminished utility in the steady state, whereas others maintain their effectiveness even at equilibrium. These results stress the importance of judiciously selecting interactions adapted to specific estimation objectives and operational regimes.