Reviving the precision of multiple entangled probes in an open system by simple $π$-pulse sequences

Abstract: Quantum metrology with entangled states in realistic noisy environments always suffers from decoherence. Therefore, the measurement precision is greatly reduced. Here we applied the dynamical decoupling method to protect the $N$-qubit quantum metrology protocol and successfully revived the scaling of the measurement precision as ${N^{-k}}$ with $k\in \left[{5/6,11/12}\right]$. The degree of the precision revival, as determined by the noise spectrum distribution, indicates that the performance of the protected protocol can be further improved by controlling the noise spectrum. Such a protected protocol is proved to be universal for entanglement-based quantum metrology in the pure dephasing and relaxation noise, which should stimulate the development of practical quantum metrology for weak signal detection of microscopic physics.