Measurement incompatibility in Bayesian quantum estimation beyond quadratic loss
Abstract
In single-shot Bayesian multiparameter quantum estimation, measurement incompatibility can increase the minimum joint quadratic loss by at most a factor of two relative to the bound obtained by optimising each parameter separately. Using the generalised Barnum--Knill inequality, we establish the same bound for a wider class of additive losses generated by positive score functions, showing that this limitation extends beyond the standard quadratic setting. To illustrate this result, we consider a broad family of periodic losses, including the sine loss sometimes employed in interferometry, and derive the corresponding incompatibility bound for Bayesian multiphase estimation with arbitrary prior knowledge. We further extend the framework to unbounded losses, such as absolute losses; this also recovers the case of quadratic losses.
Related
- Measurement incompatibility and noiseless quantum codes
- Destroying and Preserving Measurement Incompatibility over a Quantum Channel
- Quantum Estimation under Decoherence in Neutrino Oscillations: Quantum Resources, Flavor Accessibility, and Multiparameter Incompatibility
- Conjugate measurement-induced evolution towards maximally mixed states in quadratic quantum systems
- Fidelity Estimation to a Known Quantum State Is Nearly Quadratic in the Smaller Rank
BibTeX
@misc{albarelli2026measurement,
title = {{Measurement incompatibility in Bayesian quantum estimation beyond quadratic loss}},
author = {Francesco Albarelli and Stefano Chessa and Jesús Rubio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28070},
eprint = {2610.28070},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28070},
}
RIS
TY - UNPB
TI - Measurement incompatibility in Bayesian quantum estimation beyond quadratic loss
AU - Francesco Albarelli
AU - Stefano Chessa
AU - Jesús Rubio
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28070
UR - https://arxiv.org/abs/2610.28070
AB - In single-shot Bayesian multiparameter quantum estimation, measurement incompatibility can increase the minimum joint quadratic loss by at most a factor of two relative to the bound obtained by optimising each parameter separately. Using the generalised Barnum--Knill inequality, we establish the same bound for a wider class of additive losses generated by positive score functions, showing that this limitation extends beyond the standard quadratic setting. To illustrate this result, we consider a broad family of periodic losses, including the sine loss sometimes employed in interferometry, and derive the corresponding incompatibility bound for Bayesian multiphase estimation with arbitrary prior knowledge. We further extend the framework to unbounded losses, such as absolute losses; this also recovers the case of quadratic losses.
ER -