Title : Enhancement of quantum sensing via quantum memory
Abstract:
Quantum sensing uses quantum coherence and open-system dynamics to estimate physical parameters with precision beyond classical limits. However, realistic quantum sensors inevitably interact with their surrounding environments, which can degrade coherence and reduce metrological performance. In this work, we show that environmental memory, usually treated as a source of noise, can instead be engineered as a resource for enhancing quantum sensing precision. We study a hierarchical open quantum system consisting of a qubit probe coupled to a single-mode cavity, with the cavity coupled to a structured reservoir. This configuration allows the probe dynamics to transition between Markovian and non-Markovian regimes depending on the reservoir bandwidth, coupling strengths, and environmental memory time. The sensing precision is quantified using Quantum Fisher Information (QFI), while non-Markovianity is measured through information backflow, defined by positive increases in the trace distance between initially distinct quantum states.
To analyze this system, we developed MATLAB simulations combining analytical pole-residue solutions for the qubit amplitude with numerical calculations of QFI and non-Markovianity. The reduced qubit density matrix was reconstructed from the dynamical amplitude, and QFI was computed using the spectral formula with finite-difference derivatives with respect to a general system parameter. We then performed parameter sweeps and phase-diagram analysis to compare the maximum achievable QFI with the total amount of non-Markovian information backflow. Our results show that peaks in information backflow coincide with peaks in QFI, indicating that non-Markovian dynamics can directly improve sensing precision. Phase diagrams further reveal that longer reservoir memory, corresponding to smaller reservoir bandwidth, generally increases both non-Markovianity and maximum QFI. However, the relationship is not determined only by the total amount of non-Markovianity: different parameter combinations can produce the same non-Markovianity while yielding different maximum QFI values. In particular, reservoir memory plays the dominant role in enhancing QFI, while qubit-cavity coupling has a secondary effect. We also find a trade-off between precision and sensing time, since stronger memory can increase the maximum QFI but delay the time required to reach it. These results clarify how structured environments can be designed to convert quantum memory effects into metrological advantage, offering insight for future quantum sensors operating in realistic open-system settings.
