Universal shot-noise limit for quantum metrology with local Hamiltonians
- URL: http://arxiv.org/abs/2308.03696v2
- Date: Wed, 6 Mar 2024 17:44:41 GMT
- Title: Universal shot-noise limit for quantum metrology with local Hamiltonians
- Authors: Hai-Long Shi, Xi-Wen Guan, and Jing Yang
- Abstract summary: We derive a universal and fundamental bound for the growth of the quantum Fisher information.
We prove that the precision cannot surpass the shot noise limit at all times in locally interacting quantum systems.
- Score: 2.624076371876711
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum many-body interactions can induce quantum entanglement among
particles, rendering them valuable resources for quantum-enhanced sensing. In
this work, we derive a universal and fundamental bound for the growth of the
quantum Fisher information. We apply our bound to the metrological protocol
requiring only separable initial states, which can be readily prepared in
experiments. By establishing a link between our bound and the Lieb-Robinson
bound, which characterizes the operator growth in locally interacting quantum
many-body systems, we prove that the precision cannot surpass the shot noise
limit at all times in locally interacting quantum systems. This conclusion also
holds for an initial state that is the non-degenerate ground state of a local
and gapped Hamiltonian. These findings strongly hint that when one can only
prepare separable initial states, nonlocal and long-range interactions are
essential resources for surpassing the shot noise limit. This observation is
confirmed through numerical analysis on the long-range Ising model. Our results
bridge the field of many-body quantum sensing and operator growth in many-body
quantum systems and open the possibility to investigate the interplay between
quantum sensing and control, many-body physics and information scrambling
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