1. Optimal limits of continuously monitored thermometers and their Hamiltonian structure
- Author
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Mehboudi, Mohammad, Meier, Florian, Huber, Marcus, and Miller, Harry J. D.
- Subjects
Quantum Physics - Abstract
The temperature of a bosonic/fermionic environment can be measured by coupling a fully characterised $N$-dimensional probe to it. While prepare-measure-reset strategies offer optimal thermometry precision, they overlook the required time for the preparation and reset, and require excessive control of the probe at all times. Continuously monitored probes are more practical in this sense, as they take into account finite-time limitations. Thus, we study the ultimate limits and the optimal structure of continuously monitored $N$-dimensional thermometers. With the local estimation scheme our figure of merit is the Fisher information, which inversely bounds the mean square error. We provide an optimal strategy for both fermionic and bosonic environments. Under reasonable assumptions it turns out that the optimal thermometer is an effective two-level system, with a degeneracy of the ground state that increases with $N$ -- contrary to the optimal thermometers at equilibrium that have a single ground state degeneracy. The optimal gap also differs from the equilibrium case, as it depends on the bath type (fermionic/bosonic) and the specific spectral density. For $N\gg 1$, the Fisher information can grow linearly with $N$ regardless of bath type, significantly improving the well-known $\log^2 N$ scaling for equilibrium thermometry. Another remarkable observation is that the scaling with $N$ does not vanish in presence of prior ignorance, i.e., in a Bayesian setup even non-adaptive strategies can lead to an estimation error that scales with $1/N$. In comparison, a no-go theorem prohibits the ultimate equilibrium scaling $1/\log^2 N$ without adaptive strategies., Comment: Any feedback/comments are very wellcome
- Published
- 2024