Bayesian stepwise estimation of qubit rotations
Year: 2026
Authors: Manrique M., Barbieri M., Di Vizio A., Parisi M., Bizzarri G., Gianani I., Paris M.G.A.
Autors Affiliation: Univ Roma Tre, Dipartimento Sci, Via Vasca Navale 84, I-00146 Rome, Italy; Ist Nazl Ott CNR, Largo E Fermi 6, I-50125 Florence, Italy; Ist Nazl Fis Nucl, Sez Roma Tre, Via Vasca Navale 84, I-00146 Rome, Italy; Univ Milan, Dipartimento Fis Aldo Pontremoli, I-20133 Milan, Italy.
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 an SE protocol using polarization 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.
Journal/Review: AVS QUANTUM SCIENCE
Volume: 8 (2) Pages from: 24401-1 to: 24401-6
More Information: We thank Valeria Cimini, Marco G. Genoni, Matteo Rosati, and Vittorio Giovannetti for useful discussion. This work has been realized with the support of the PRIN project PRIN22-RISQUE-2022T25TR3 of the Italian Ministry of University. G.B. and M.B. are supported by the Rome Technopole Innovation Ecosystem (PNRR grant M4-C2-Inv). I.G. and M.B. acknowledge the support from MUR Dipartimento di Eccellenza 2023-2027.DOI: 10.1116/5.0308988
