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The diverging responses to parameter variations of systems at quantumcritical points motivate schemes of quantum metrology that featuresub-Heisenberg scaling of the sensitivity with the system size (e.g., thenumber of particles). This sensitivity enhancement is fundamentally rooted inthe formation of Schr\"odinger cat states, or macroscopic superposition statesat the quantum critical points. The cat states, however, are fragile todecoherence caused by local noises on individual particles or coupling to localenvironments, since the local decoherence of any particle would cause thecollapse of the whole cat state. Therefore, it is unclear whether thesub-Heisenberg scaling of quantum critical metrology is robust against thelocal decoherence. Here we study the effects of local decoherence on thequantum critical metrology, using a one-dimensional transverse-field Isingmodel as a representative example. Based on a previous work [Phys. Rev. Lett.94, 047201 (2005)] on the critical behaviors of the noisy Ising model, whichshows that the universality class of the quantum criticality is modified by thedecoherence, we find that the standard quantum limit is recovered by thesingle-particle decoherence, which is equivalent to local quantum measurementconducted by the environment and destroys the many-body entanglement in theground state at the quantum critical point. Following the renormalization groupanalysis [Phys. Rev. B 69, 054426 (2004)], we argue that the noise effects onquantum critical metrology should be universal. This works demonstrates theimportance of protecting macroscopic quantum coherence for quantum sensingbased on critical behaviors.

Effects of local decoherence on quantum critical metrology