Universal shot-noise limit for quantum metrology with local Hamiltonians

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

Close to the published version

References in corpus (24)

• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Generalized Limits for Single-Parameter Quantum Estimation
• Using entanglement against noise in quantum metrology
• Quantum criticality as a resource for quantum estimation
• Quantum chaos and the complexity of spread of states
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Operator complexity: a journey to the edge of Krylov space
• Geometry of quantum phase transitions
• Dynamic framework for criticality-enhanced quantum sensing
• On quantumness in multi-parameter quantum estimation
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• Entanglement, avoided crossings and quantum chaos in an Ising model with a tilted magnetic field
• Global sensing and its impact for quantum many-body probes with criticality
• Experimental demonstration of continuous quantum error correction
• Fundamental Sensitivity Limits for non-Hermitian Quantum Sensors
• Fast and high-fidelity state preparation and measurement in triple-quantum-dot spin qubits
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• High fidelity state preparation and measurement of ion hyperfine qubits with I > 1/2
• Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
• Variational principle for optimal quantum controls in quantum metrology
• Strong quantum metrological limit from many-body physics
• Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied
• Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain
• Quantum metrology including state preparation and readout times

Cited by in corpus (10)

• Review: Quantum Metrology and Sensing with Many-Body Systems
• Estimation of Hamiltonian parameters from thermal states
• Quantum delocalization on correlation landscape: The key to exponentially fast multipartite entanglement generation
• Heisenberg-limited metrology with perturbing interactions
• Multicritical quantum sensors driven by symmetry-breaking
• From dynamical to steady-state many-body metrology: Precision limits and their attainability with two-body interactions
• Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
• Quantum Measurement Encoding for Quantum Metrology
• Optimal Local Measurements in Single-Parameter Quantum Metrology
• Approaching the double-Heisenberg scaling sensitivity in the Tavis-Cummings model