Uninformed Bayesian Quantum Thermometry

Abstract

We study the Bayesian approach to thermometry with no prior knowledge about the expected temperature scale, through the example of energy measurements on fully or partially thermalized qubit probes. We show that the most common Bayesian estimators, namely the mean and the median, lead to high-temperature divergences when used for uninformed thermometry. To circumvent this and achieve better overall accuracy, we propose two new estimators based on an optimization of relative deviations. Their global temperature-averaged behavior matches a modified van Trees bound, which complements the Cramér-Rao bound for smaller probe numbers and unrestricted temperature ranges. Furthermore, we show that, using partially thermalized probes, one can increase the range of temperatures to which the thermometer is sensitive at the cost of the local accuracy.

12 pages, 8 figures, v2: corrected conversion of the logarithmic error, v3: citations added

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Cited by in corpus (17)

• Low-temperature quantum thermometry boosted by coherence generation
• Optimal cold atom thermometry using adaptive Bayesian strategies
• Roadmap on Quantum Thermodynamics
• Multi-spin probes for thermometry in the strong-coupling regime
• Sub-nK thermometry of an interacting $d$-dimensional homogeneous Bose gas
• Quantum scale estimation
• Thermometry by correlated dephasing of impurities in a 1D Fermi gas
• Probe thermometry with continuous measurements
• Energy measurements remain thermometrically optimal beyond weak coupling
• Metrological symmetries in singular quantum multi-parameter estimation
• Bayesian estimation for collisional thermometry
• Topological quantum thermometry
• On the role of symmetry and geometry in global quantum sensing
• Optimal limits of continuously monitored thermometers and their Hamiltonian structure
• Correlated decoherence and thermometry with mobile impurities in a 1D Fermi gas
• The Cramér-Rao approach and global quantum estimation of bosonic states
• Nonequilibrium thermometry via an ensemble of initially correlated qubits