Universal Shot-Noise Limit for Quantum Metrology with Local Hamiltonians

Shi, Hai LongInnovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China; QSTAR and INO-CNR, Largo Enrico Fermi 2, 50125 Firenze, Italy; Hefei National Laboratory, Hefei 230088, China (author)

QC 20240314
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.

Guan, Xi WenInnovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China; Hefei National Laboratory, Hefei 230088, China; Department of Fundamental and Theoretical Physics, Research School of Physics, Australian National University, Canberra ACT 0200, Australia (author)
Yang, JingStockholms universitet,Nordiska institutet för teoretisk fysik (Nordita)(Swepub:su)jiya5375 (author)
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China; QSTAR and INO-CNR, Largo Enrico Fermi 2, 50125 Firenze, Italy; Hefei National Laboratory, Hefei 230088, ChinaInnovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China; Hefei National Laboratory, Hefei 230088, China; Department of Fundamental and Theoretical Physics, Research School of Physics, Australian National University, Canberra ACT 0200, Australia (creator_code:org_t)

In:Physical Review Letters: American Physical Society (APS)132:100031-90071079-7114

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Physical Science ...; and Condensed Matter ...

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