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.

Reference: Yaoming Chu, Xiangbei Li and Jianming Cai,

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.170801