Multiparameter quantum estimation with a uniformly accelerated Unruh-DeWitt detector
Phys. Rev. A 114, 052417 – Published 5 November, 2026
DOI: https://doi.org/10.1103/6qbj-wspr
Abstract
The uniformly accelerated Unruh-DeWitt detector serves as a fundamental model in relativistic quantum metrology. While previous studies have mainly concentrated on single-parameter estimation via the quantum Cramér-Rao bound, the multiparameter case remains significantly underexplored. In this paper, we investigate the multiparameter estimation for a uniformly accelerated Unruh-DeWitt detector coupled to a vacuum scalar field in both bounded and unbounded Minkowski vacuum. Our analysis reveals that the quantum Cramér-Rao bound fails to provide a tight error bound for the two-parameter estimation involving the initial phase and weight parameters. For this reason, we numerically compute two tighter error bounds, the Holevo Cramér-Rao bound and the Nagaoka bound, based on a semidefinite program. Notably, our results demonstrate that the Nagaoka bound yields the tightest error bound among all the bounds considered and is attained by the four-outcome positive-operator-valued measures constructed, consistent with the general hierarchy of multiparameter quantum estimation. In the case with a boundary, we observe the introduction of a boundary systematically reduces the values of both the Holevo Cramér-Rao bound and the Nagaoka bound, indicating an improvement on the attainable estimation precision. These results offer valuable insights on and practical guidance for advancing multiparameter estimation in relativistic context.
