Bayesian stepwise estimation of qubit rotations

TL;DR

This paper evaluates Bayesian stepwise estimation for qubit rotations, showing it performs well with simple measurements but does not surpass joint estimation in ultimate precision due to prior averaging effects.

Contribution

It provides an experimental comparison of Bayesian stepwise and joint estimation methods for qubit rotations, highlighting practical advantages and limitations.

Findings

SE achieves near-classical bounds with simple measurements

Averaging over priors negates asymptotic SE advantage

Stepwise strategy is practically beneficial with fixed measurements

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.