Quantum scale estimation

Abstract

Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology, since current practice focuses almost exclusively on the estimation of phase and location parameters. For given prior probability and quantum state, and using Bayesian principles, a rule to construct the optimal probability-operator measurement is provided. Furthermore, the corresponding minimum mean logarithmic error is identified. This is then generalised as to accommodate the simultaneous estimation of multiple scale parameters, and a procedure to classify practical measurements into optimal, almost-optimal or sub-optimal is highlighted. As a means of illustration, the new framework is exploited to generalise scale-invariant global thermometry, as well as to address the estimation of the lifetime of an atomic state. On a more conceptual note, the optimal strategy is employed to construct an observable for scale parameters, an approach which may serve as a template for a more systematic search of quantum observables. Quantum scale estimation thus opens a new line of enquire - the precise measurement of scale parameters such as temperatures and rates - within the quantum information sciences.

17 pages, 1 figure, 1 table. New example addressing the quantum estimation of the lifetime of an atomic state. Other minor corrections

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Cited by in corpus (13)

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• Current Trends in Global Quantum Metrology
• Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations
• Invasiveness of non-equilibrium quantum thermometry
• On the optimality of the radical-pair quantum compass
• Probe thermometry with continuous measurements
• First-principles construction of symmetry-informed quantum metrologies
• Energy measurements remain thermometrically optimal beyond weak coupling
• Saturable global quantum sensing
• On the role of symmetry and geometry in global quantum sensing
• Bayesian minimum mean square error for transmissivity sensing
• Optimal limits of continuously monitored thermometers and their Hamiltonian structure
• Adaptive, symmetry-informed Bayesian metrology for precise quantum technology measurements