Fundamental Limits in Bayesian Thermometry and Attainability via Adaptive Strategies

Mohammad Mehboudi*, Mathias R. Jørgensen*, Stella Seah, Jonatan B. Brask, Jan Kołodyński, Martí Perarnau-Llobet*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


We investigate the limits of thermometry using quantum probes at thermal equilibrium within the Bayesian approach. We consider the possibility of engineering interactions between the probes in order to enhance their sensitivity, as well as feedback during the measurement process, i.e., adaptive protocols. On the one hand, we obtain an ultimate bound on thermometry precision in the Bayesian setting, valid for arbitrary interactions and measurement schemes, which lower bounds the error with a quadratic (Heisenberg-like) scaling with the number of probes. We develop a simple adaptive strategy that can saturate this limit. On the other hand, we derive a no-go theorem for nonadaptive protocols that does not allow for better than linear (shot-noise-like) scaling even if one has unlimited control over the probes, namely, access to arbitrary many-body interactions.
Original languageEnglish
Article number130502
JournalPhysical Review Letters
Issue number13
Number of pages7
Publication statusPublished - 2022


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