We address the characterization of two-qubit gates, focusing on bounds to precision in the joint estimation of the three parameters that define their Cartan decomposition. We derive the optimal probe states that jointly maximize precision, minimize sloppiness, and eliminate quantum incompatibility. Additionally, we analyze the properties of the set of optimal probes and evaluate their robustness against noise.
@article{arxiv.2502.08379,
title = {Cartan Quantum Metrology},
author = {Gabriele Fazio and Jiayu He and Matteo G. A. Paris},
journal= {arXiv preprint arXiv:2502.08379},
year = {2025}
}