Universal Shot-Noise Limit for Quantum Metrology with Local Hamiltonians

Year: 2024

Authors: Shi HL., Guan XW., Yang J.

Autors Affiliation: Chinese Acad Sci, Innovat Acad Precis Measurement Sci & Technol, Wuhan 430071, Peoples R China; QSTAR, Largo Enr Fermi 2, I-50125 Florence, Italy; CNR, INO, Largo Enr Fermi 2, I-50125 Florence, Italy; Hefei Natl Lab, Hefei 230088, Peoples R China; Australian Natl Univ, Res Sch Phys, Dept Fundamental & Theoret Phys, Canberra, ACT 0200, Australia; Stockholm Univ, KTH Royal Inst Technol, Nordita, Hannes Alfvens Vag 12, S-10691 Stockholm, Sweden.

Abstract: Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we establish a link between the bound on the growth of the quantum Fisher information and the Lieb-Robinson bound, which characterizes the operator growth in locally interacting quantum many-body systems. We show that for initial separable states, despite the use of local many-body interactions, the precision cannot surpass the shot noise limit at all times. This conclusion also holds for an initial state that is the nondegenerate 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.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 132 (10)      Pages from: 100803-1  to: 100803-7

More Information: We thank Adolfo del Campo for useful comments on the manuscript. It is a pleasure to acknowledge feedback from Federcio Balducci, Wenchao Ge, Jiru Liu, Xingze Qiu, and Hong-Hao Tu. X. W. G. was supported by the NSFC key Grants No. 92365202, No. 12134015, No. 12121004, and partially supported by the Innovation Program for Quantum Science and Technology 2021ZD0302000. H. L. S. was supported by the European Commission through the H2020 QuantERA ERA -NET Cofund in Quantum Technologies project MENTA and the Hefei National Laboratory. J. Y. was funded by the Wallenberg Initiative on Networks and Quantum Information (WINQ) and would like to thank Hui Zhai for the hospitality in hosting his visit at the Institute of Advanced Study in Tsinghua University, during which this work was completed.
KeyWords: Model
DOI: 10.1103/PhysRevLett.132.100803

Citations: 1
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