Restoring Heisenberg-Limited Precision in Non-Markovian Open Quantum Systems via Dynamical Decoupling

Non-classical resources enable measurements to achieve a precision that exceeds the limits predicted by the central limit theorem. However, environmental noise arising from system-environment interactions severely limits the performance of such resources through decoherence. While significant progress has been made in mitigating Markovian noise, the extent to which non-Markovian noise can be mitigated remains poorly understood. We demonstrate that Heisenberg Scaling, the ultimate quantum limit on measurement precision, can be recovered in quantum metrology under non-Markovian noise by leveraging carefully designed Dynamical Decoupling Techniques. Importantly, our approach does not rely on assumptions of Markovian dynamics. By imposing appropriate conditions on the control Hamiltonian, we show that HS can be achieved irrespective of whether the noise is Markovian or non-Markovian. We also prove necessary and sufficient conditions for the existence of such control Hamiltonians. As an illustrative example, we apply our framework to the damped Jaynes-Cummings model, successfully mitigating memory effects and maintaining measurement precision in complex, non-Markovian environments. These findings highlight the power of quantum control to overcome decoherence challenges and enhance metrological performance in realistic, noisy quantum systems.