Enhancing the parameter estimation precision in a damped system by square-wave modulation

The quantum Fisher information (QFI) plays a key role in quantum metrological scenarios, and can be enhanced by certain entanglement protocols. In this work, we focus on the maximal mean QFI for L qubits, and study how a dynamical decoupling scheme rescues the entanglement-assisted QFI, which would be rapidly damaged by decoherence without such a scheme. We found that the square-wave modulation for the transition frequency of the qubit can be settled in a recursive transfer matrix form thus both periodic and random pulse sequences can be investigated exactly by assuming that the spectral density of the reservoir is Lorentzian. Considering the Greenberger-Horne-Zeilinger state as an initial state of L qubits imbedded in the independent damping channels, the use of additional square-wave pulse sequences allows the Heisenberg scaling to be restored for parameterestimation precision. How to optimize the pulse parameters with certain pulse energies should be carefully treated. The analyzability of the modulated damping dynamics may provide a potential start point for defeating decoherence in quantum information processing.