Fundamental Limits in Bayesian Thermometry and Attainability via Adaptive Strategies

Area of Science:

• Quantum Metrology
• Statistical Mechanics
• Information Theory

Background:

• Thermometry, the science of accurate temperature measurement, is crucial in various scientific fields.
• Quantum probes offer enhanced sensitivity for precise measurements.
• The Bayesian approach provides a framework for statistical inference in parameter estimation.

Purpose of the Study:

• To determine the ultimate limits of thermometry precision using quantum probes under thermal equilibrium within the Bayesian framework.
• To investigate the impact of engineered interactions and adaptive measurement protocols on thermometry sensitivity.
• To establish fundamental bounds on precision achievable with quantum thermometry.

Main Methods:

• Utilizing the Bayesian approach to derive fundamental bounds on thermometry precision.
• Analyzing the effects of engineered probe interactions and adaptive measurement strategies.
• Developing and evaluating specific adaptive protocols to assess achievable precision limits.

Main Results:

• An ultimate bound on Bayesian thermometry precision is established, showing a quadratic (Heisenberg-like) scaling with the number of probes for arbitrary interactions and measurement schemes.
• A simple adaptive strategy is demonstrated to saturate this ultimate bound.
• A no-go theorem is derived for nonadaptive protocols, proving that precision is limited to linear (shot-noise-like) scaling, irrespective of interaction complexity.

Conclusions:

• Adaptive quantum thermometry protocols, combined with engineered interactions, can achieve Heisenberg-limited precision.
• Nonadaptive protocols fundamentally limit thermometry precision to shot-noise scaling, regardless of probe interaction complexity.
• The findings provide crucial insights into optimizing quantum-enhanced temperature measurements.