On the role of symmetry and geometry in global quantum sensing

• URL: http://arxiv.org/abs/2502.14817v2
• Date: Sat, 02 Aug 2025 00:11:41 GMT
• Title: On the role of symmetry and geometry in global quantum sensing
• Authors: Julia Boeyens, Jonas Glatthard, Edward Gandar, Stefan Nimmrichter, Luis A. Correa, Jesús Rubio,
• Abstract summary: Global quantum sensing enables parameter estimation across arbitrary ranges with a finite number of measurements.<n>There are two fundamentally different ways to capture prior ignorance and uninformed estimation.<n>We show how to apply the two approaches in relevant examples of rate and coherence estimation in noisy settings.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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