On the role of symmetry and geometry in global quantum sensing
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908579874734080 |
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| author | Boeyens, Julia Glatthard, Jonas Gandar, Edward Nimmrichter, Stefan Correa, Luis A. Rubio, Jesús |
| author_facet | Boeyens, Julia Glatthard, Jonas Gandar, Edward Nimmrichter, Stefan Correa, Luis A. Rubio, Jesús |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the role of symmetry and geometry in global quantum sensing Boeyens, Julia Glatthard, Jonas Gandar, Edward Nimmrichter, Stefan Correa, Luis A. Rubio, Jesús Quantum Physics Mathematical Physics Data Analysis, Statistics and Probability 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. |
| title | On the role of symmetry and geometry in global quantum sensing |
| topic | Quantum Physics Mathematical Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2502.14817 |