Strong quantum metrological limit from many-body physics

TL;DR

This paper establishes a fundamental speed limit for quantum Fisher information growth in many-body systems, linking quantum dynamics to metrological precision limits and constraining the attainability of the Heisenberg limit.

Contribution

It introduces a universal speed limit based on Lieb-Robinson bounds that accounts for the complexity of preparing quantum resource states in many-body systems.

Findings

Sets a fundamental precision limit considering resource state preparation complexity.

Identifies key features of many-body systems crucial for quantum advantage.

Connects many-body quantum dynamics with quantum metrology constraints.

Abstract

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.