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.

量子Fisher信息（QFI）在量子计量方案中起着关键作用，并且可以通过某些纠缠协议进行增强。在这项工作中，我们专注于L个量子比特的最大平均QFI ，并研究动态解耦方案如何挽救纠缠辅助QFI，如果没有这种方案，它们会因去相干而迅速受损。我们发现，可以以递归传递矩阵形式来确定用于qubit跃迁频率的方波调制，因此可以通过假设储层的频谱密度为洛伦兹式来精确地研究周期性脉冲序列和随机脉冲序列。将格林伯格-霍恩-泽林格状态视为L的初始状态嵌入独立阻尼通道中的量子比特，使用额外的方波脉冲序列可以恢复Heisenberg缩放比例，以实现参数估计精度。应该谨慎对待如何优化具有某些脉冲能量的脉冲参数。调制阻尼动力学的可分析性可以为克服量子信息处理中的退相干提供潜在的起点。