Universal shot-noise limit for quantum metrology with local Hamiltonians
arXiv:2308.03696 · doi:10.1103/PhysRevLett.132.100803
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
arXiv commentClose to the published version
References in corpus (48)
- Quantum sensing
- Advances in Quantum Metrology
- Quantum metrology
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- Quantum Fisher information matrix and multiparameter estimation
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Fisher information and multiparticle entanglement
- Multipartite entanglement and high precision metrology
- Quantum enhanced measurements without entanglement
- Generalized Limits for Single-Parameter Quantum Estimation
- Using entanglement against noise in quantum metrology
- A Universal Operator Growth Hypothesis
- Quantum criticality as a resource for quantum estimation
- Quantum Brachistochrone
- Quantum chaos and the complexity of spread of states
- Critical Quantum metrology with a finite-component quantum phase transition
- Fidelity susceptibility, scaling, and universality in quantum critical phenomena
- Operator complexity: a journey to the edge of Krylov space
- Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
- Geometry of quantum phase transitions
- Dynamic framework for criticality-enhanced quantum sensing
- On The Evolution Of Operator Complexity Beyond Scrambling
- Exponentially Enhanced Quantum Metrology
- Quantum metrology for a general Hamiltonian parameter
- Locality in Quantum and Markov Dynamics on Lattices and Networks
- On quantumness in multi-parameter quantum estimation
- Quantum critical metrology
- At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
- Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
- Universal time scaling for Hamiltonian parameter estimation
- Nonlinear quantum metrology of many-body open systems
- Entanglement, avoided crossings and quantum chaos in an Ising model with a tilted magnetic field
- Geometric Speed Limit of Accessible Many-Body State Preparation
- Global sensing and its impact for quantum many-body probes with criticality
- Quantum metrology with a quantum-chaotic sensor
- 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
- Quantum parameter estimation with the Landau-Zener transition
- Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain
- Uhlmann number in translational invariant systems
- 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