Bayesian stepwise estimation of qubit rotations

• URL: http://arxiv.org/abs/2512.04898v1
• Date: Thu, 04 Dec 2025 15:26:06 GMT
• Title: Bayesian stepwise estimation of qubit rotations
• Authors: Mylenne Manrique, Marco Barbieri, Assunta Di Vizio, Miranda Parisi, Gabriele Bizzarri, Ilaria Gianani, Matteo G. A. Paris,
• Abstract summary: We investigate stepwise estimation (Se) for measuring the two parameters of a unitary qubit rotation.<n>While analysis predicts a precision advantage for SE over joint estimation (JE) in regimes where the quantum Fisher information matrix is near-singular ("sloppy" models)<n>We demonstrate that this advantage is mitigated within a practical Bayesian framework with limited resources.
• Score: 0.15650076339927835
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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