  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 time 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 in a generic many-body lattice system with bounded one-site energy. It
enables us to identify the essential features of quantum many-body systems that
are crucial for achieving the quantum advantage of quantum metrology, and
brings an interesting connection between many-body quantum dynamics and quantum
metrology.
