Bayesian stepwise estimation of qubit rotations
Abstract
This work investigates Bayesian stepwise estimation (Se) for measuring the two parameters of a unitary qubit rotation. While asymptotic analysis predicts a precision advantage for SE over joint estimation (JE) in regimes where the quantum Fisher information matrix is near-singular ("sloppy" models), we demonstrate that this advantage is mitigated within a practical Bayesian framework with limited resources. We experimentally implement a SE protocol using polarisation qubits, achieving uncertainties close to the classical Van Trees bounds. However, comparing the total error to the ultimate quantum Van Trees bound for JE reveals that averaging over prior distributions erases the asymptotic SE advantage. Nevertheless, the stepwise strategy retains a significant practical benefit as it operates effectively with simple, fixed measurements, whereas saturating the JE bound typically requires complex, parameter-dependent operations.
Cite
@article{arxiv.2512.04898,
title = {Bayesian stepwise estimation of qubit rotations},
author = {Mylenne Manrique and Marco Barbieri and Assunta Di Vizio and Miranda Parisi and Gabriele Bizzarri and Ilaria Gianani and Matteo G. A. Paris},
journal= {arXiv preprint arXiv:2512.04898},
year = {2025}
}