On the role of symmetry and geometry in global quantum sensing
arXiv:2502.14817 · doi:10.1088/2058-9565/ae08e1
Abstract
Global quantum sensing enables parameter estimation across arbitrary ranges with a finite number of measurements. Among the various existing formulations, the Bayesian paradigm stands as a flexible approach for optimal protocol design under minimal assumptions. Within this paradigm, however, there are two fundamentally different ways to capture prior ignorance and uninformed estimation; namely, requiring invariance of the prior distribution under specific parameter transformations, or adhering to the geometry of a state space. In this paper we carefully examine the practical consequences of both the invariance-based and the geometry-based approaches, and show how to apply them in relevant examples of rate and coherence estimation in noisy settings. We find that, while the invariance-based approach often leads to simpler priors and estimators and is more broadly applicable in adaptive scenarios, the geometry-based one can lead to faster posterior convergence in a well-defined measurement setting. Crucially, by employing the notion of location-isomorphic parameters, we are able to unify the two formulations into a single practical and versatile framework for optimal global quantum sensing, detailing when and how each set of assumptions should be employed to tackle any given estimation task. We thus provide a blueprint for the design of novel high-precision quantum sensors.
19 pages, 7 figures. Accepted version
References in corpus (36)
- Optimal Quantum Phase Estimation
- Quantum Metrology for Gravitational Wave Astronomy
- Individual quantum probes for optimal thermometry
- Group-Invariant Quantum Machine Learning
- Mechanical Quantum Sensing in the Search for Dark Matter
- Quantum sensing with atomic, molecular, and optical platforms for fundamental physics
- Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements
- Experimental progress on quantum coherence: detection, quantification, and manipulation
- Bayesian estimation of one-parameter qubit gates
- Massive quantum systems as interfaces of quantum mechanics and gravity
- Macroscopic quantum test with bulk acoustic wave resonators
- Optimal Probes for Global Quantum Thermometry
- Fundamental limits in Bayesian thermometry and attainability via adaptive strategies
- Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology
- Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound
- Optimal cold atom thermometry using adaptive Bayesian strategies
- Quantum parameter estimation in a dissipative environment
- Uninformed Bayesian Quantum Thermometry
- Measuring kinetic parameters using quantum plasmonic sensing
- Comparing transient oligonucleotide hybridization kinetics using DNA-PAINT and optoplasmonic single-molecule sensing on gold nanorods
- Experimental measurement of kinetic parameters using quantum plasmonic sensing
- Quantum scale estimation
- Large-Scale Atom Interferometry for Fundamental Physics
- Current Trends in Global Quantum Metrology
- Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations
- Quantum metrology using quantum combs and tensor network formalism
- Hierarchies of Frequentist Bounds for Quantum Metrology: From Cramér-Rao to Barankin
- Quantum metrology in the finite-sample regime
- Controlling the interactions in a cold atom quantum impurity system
- First Search for Ultralight Dark Matter Using a Magnetically Levitated Particle
- Only Classical Parameterised States have Optimal Measurements under Least Squares Loss
- Benchmarking Bayesian quantum estimation
- First-principles construction of symmetry-informed quantum metrologies
- Testing collapse models with Bose-Einstein-Condensate interferometry
- Bayesian inference for near-field interferometric tests of collapse models
- Bayesian and frequentist estimators for the transition frequency of a driven two-level quantum system