The diverging responses to parameter variations of systems at quantum critical points motivate schemes of quantum critical metrology (QCM), which feature sub-Heisenberg scaling of the sensitivity with the system size (e.g., the number of particles). This sensitivity enhancement by quantum criticality is rooted in the formation of Schrödinger cat states, or macroscopic superposition states at the quantum critical points. The cat states, however, are fragile to decoherence caused by coupling to local environments, since the local decoherence of any particle would cause the collapse of the whole cat state. Therefore, it is unclear whether the sub-Heisenberg scaling of QCM is robust against the local decoherence. Here we study the effects of local decoherence on QCM, using a one-dimensional transverse-field Ising model as a representative example. We find that the standard quantum limit is recovered by single-particle decoherence. Using renormalization group analysis, we demonstrate that the noise effects on QCM is general and applicable to many universality classes of quantum phase transitions whose low-energy excitations are described by a ${\varphi }^4$ effective field theory. Since in general the many-body entanglement of the ground states at critical points, which is the basis of QCM, is fragile to quantum measurement by local environments, we conjecture that the recovery of the standard quantum limit by local decoherence is universal for QCM using phase transitions induced by the formation of long-range order. This work demonstrates the importance of protecting macroscopic quantum coherence for quantum sensing based on critical behaviors.

中文翻译：

---

局部退相干对量子临界计量的影响

在量子临界点对系统参数变化的不同响应激发了量子临界计量 (QCM) 方案，其特征是灵敏度随系统尺寸（例如，粒子数）的亚海森堡标度。这种由量子临界引起的灵敏度增强源于薛定谔猫态或量子临界点处的宏观叠加态的形成。然而，猫状态对于耦合到局部环境引起的退相干很脆弱，因为任何粒子的局部退相干都会导致整个猫状态的崩溃。因此，尚不清楚 QCM 的亚海森堡标度是否对局部退相干具有鲁棒性。在这里，我们使用一维横向场 Ising 模型作为代表性示例研究局部退相干对 QCM 的影响。我们发现标准量子极限可以通过单粒子退相干恢复。使用重整化群分析，我们证明了 QCM 上的噪声效应是普遍的，适用于许多普遍性类别的量子相变，其低能量激发由${\phi }^4$有效场论。由于作为 QCM 基础的临界点处基态的多体纠缠通常对局域环境的量子测量很脆弱，我们推测通过局域退相干恢复标准量子极限对于 QCM 来说是普遍的，使用由长程有序的形成引起的相变。这项工作证明了保护宏观量子相干性对于基于临界行为的量子传感的重要性。