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arXiv · 2302.14223

Bayesian Nagaoka-Hayashi Bound for Multiparameter Quantum-State Estimation Problem

Jun Suzuki
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Abstract

In this work we propose a Bayesian version of the Nagaoka-Hayashi bound when estimating a parametric family of quantum states. This lower bound is a generalization of a recently proposed bound for point estimation to Bayesian estimation. We then show that the proposed lower bound can be efficiently computed as a semidefinite programming problem. As a lower bound, we also derive a Bayesian version of the Holevo-type bound from the Bayesian Nagaoka-Hayashi bound. Lastly, we prove that the new lower bound is tighter than the Bayesian quantum Cramer-Rao bounds.

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Jun Suzuki. 2023-02-28. Bayesian Nagaoka-Hayashi Bound for Multiparameter Quantum-State Estimation Problem. https://arxiv.org/abs/2302.14223

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