From dynamical to steady-state many-body metrology: Precision limits and their attainability with two-body interactions
arXiv:2412.02754 · doi:10.1103/PRXQuantum.6.030309
Abstract
We consider the estimation of an unknown parameter via a many-body probe. The probe is initially prepared in a product state and many-body time-independent interactions enhance its -sensitivity during the dynamics and/or in the steady state. We present bounds on the Quantum Fisher Information, and corresponding optimal interacting Hamiltonians, for two paradigmatic scenarios for encoding~: (i)~via unitary Hamiltonian dynamics (dynamical metrology), and (ii)~in the Gibbs and diagonal ensembles (time-averaged dephased state), two ubiquitous steady states of many-body open dynamics. We then move to the specific problem of estimating the strength of a magnetic field via interacting spins and derive two-body interacting Hamiltonians that can approach the fundamental precision bounds. In this case, we additionally analyze the transient regime leading to the steady states and characterize tradeoffs between equilibration times and measurement precision. Overall, our results provide a comprehensive picture of the potential of many-body control in quantum sensing.
16 + 22 pages, 10 figures, 2 tables
References in corpus (68)
- Thermalization and its mechanism for generic isolated quantum systems
- Quantum metrology
- Quantum many-body systems out of equilibrium
- Nonlinear atom interferometer surpasses classical precision limit
- Atom chip based generation of entanglement for quantum metrology
- Quantum spin squeezing
- Quantum metrology from a quantum information science perspective
- Quantum limits in optical interferometry
- Quantum enhanced measurements without entanglement
- Generalized Limits for Single-Parameter Quantum Estimation
- Generalized Thermalization in an Integrable Lattice System
- Quantum criticality as a resource for quantum estimation
- Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
- Critical Quantum metrology with a finite-component quantum phase transition
- Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei
- Mixed-state fidelity and quantum criticality at finite temperature
- Thermometry in the quantum regime: Recent theoretical progress
- Dynamic framework for criticality-enhanced quantum sensing
- Quantum metrology for a general Hamiltonian parameter
- Optimal quantum estimation in spin systems at criticality
- Criticality-Enhanced Quantum Sensing via Continuous Measurement
- Relaxation of a one-dimensional Mott insulator after an interaction quench
- Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
- At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
- Quantum Metrology with Strongly Interacting Spin Systems
- Bures metric over thermal state manifolds and quantum criticality
- Exact dynamics in the inhomogeneous central-spin model
- Critical parametric quantum sensing
- Dynamical phase transitions as a resource for quantum enhanced metrology
- Quantum information-geometry of dissipative quantum phase transitions
- Entanglement and work extraction in the central-spin quantum battery
- Quantum sensing close to a dissipative phase transition: symmetry breaking and criticality as metrological resources
- Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom
- High-density quantum sensing with dissipative first order transitions
- Learning many-body Hamiltonians with Heisenberg-limited scaling
- Phase transitions in an Ising chain interacting with a single mode cavity field
- Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise
- Quantum metrology with boundary time crystals
- Quantum transition-edge detectors
- Combining critical and quantum metrology
- Frequentist and Bayesian Quantum Phase Estimation
- Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling
- Collective quantum memory activated by a driven central spin
- Variational principle for optimal quantum controls in quantum metrology
- Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point
- Strong quantum metrological limit from many-body physics
- Critical quantum metrology assisted by real-time feedback control
- Floquet Engineering to Overcome No-Go Theorem of Noisy Quantum Metrology
- Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied
- Collective advantages in finite-time thermodynamics
- Control of open quantum systems: Case study of the central spin model
- Multiparameter critical quantum metrology with impurity probes
- Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain
- Stark localization as a resource for weak-field sensing with super-Heisenberg precision
- Optimality and Noise-Resilience of Critical Quantum Sensing
- Achieving sub-shot-noise sensing at finite temperatures
- Criticality-enhanced Electric Field Gradient Sensor with Single Trapped Ions
- Localization Driven Quantum Sensing
- Saturating the quantum Cramér-Rao bound using LOCC
- Self-consistent many-body metrology
- Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing
- Modular Many-Body Quantum Sensors
- Fundamental limits of metrology at thermal equilibrium
- Optimal Thermometers with Spin Networks
- The advantage of quantum control in many-body Hamiltonian learning
- Activation of metrologically useful genuine multipartite entanglement
- Universal shot-noise limit for quantum metrology with local Hamiltonians
- Heisenberg scaling with classical long-range correlations