Strong quantum metrological limit from many-body physics
Yaoming Chu, Xiangbei Li and Jianming Cai,Phys. Rev. Lett. 130, 170801（2023）
Surpassing the standard quantum limit and even reaching the Heisenberg limit using quantum entanglement, represents the Holy Grail of quantum metrology. However, quantum entanglement is a valuable resource that does not come without a price. The exceptional overhead for the preparation of large-scale entangled states raises disconcerting concerns about whether the Heisenberg limit is fundamentally achievable. Here we find a universal speed limit set by the Lieb-Robinson light cone for the quantum Fisher information growth to characterize the metrological potential of quantum resource states during their preparation. Our main result establishes a strong precision limit of quantum metrology accounting for the complexity of many-body quantum resource state preparation and reveals a fundamental constraint for reaching the Heisenberg limit. Our result makes it possible to identify the essential features of quantum many-body systems that are crucial for achieving the quantum advantage of quantum metrology and brings a new perspective to understanding many-body quantum dynamics from quantum metrology.