General framework for estimating the ultimate precision limit in Bayesian quantum metrology

Bruno M. Escher, R. L. de Matos Filho, L. Davidovich

Rozhin Yousefjani, S. Salimi, A. S. Khorashad

Bruno M. Escher, R. L. de Matos Filho, L. Davidovich

We propose a general framework that yields useful lower bounds for ultimate limits of precision in parameter estimation for noisy systems, and describes the transition from the Heisenberg to the standard limit in optical interferometry

Francesco Albarelli, Dominic Branford, Jesús Rubio

We present a comprehensive and pedagogical formulation of Bayesian multiparameter quantum estimation. Within this framework, we analyse the role of measurement incompatibility and establish its quantitative effect on attainable precision. We achieve this by deriving upper bounds based on the pretty good measurement -- a notion from hypothesis testing -- combined with the evaluation of the Nagaoka-Hayashi lower bound. In general, we prove that, as in the many-copy regime of local estimation theory, incompatibility can at most double the minimum loss relative to the idealised scenario in which individually optimal measurements are assumed jointly implementable. Therefore, in practical situations, the latter may provide a sufficient and computationally efficient benchmark without solving the full optimisation problem. Our results, which we illustrate through applications of discrete phase imaging, phase and dephasing estimation, and qubit sensing, provide analytical and numerical tools for assessing ultimate precision limits and the role of measurement incompatibility in Bayesian multiparameter quantum metrology, including an open-source package for all the bounds discussed here.

Jagoba Apellaniz Asategui

Haidong Yuan, Chi‐Hang Fred Fung

Abstract One of the main quests in quantum metrology, and quantum parameter estimation in general, is to find out the highest achievable precision with given resources and design schemes to attain it. In this article we present a general framework for quantum parameter estimation and provide systematic methods for computing the ultimate precision limit, which is more general and efficient than conventional methods.