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

• URL: http://arxiv.org/abs/2302.14223v2
• Date: Mon, 26 Jun 2023 06:14:15 GMT
• Title: Bayesian Nagaoka-Hayashi Bound for Multiparameter Quantum-State Estimation Problem
• Authors: Jun Suzuki
• Abstract summary: We show that the proposed lower bound can be efficiently computed as a semidefinite programming problem. We prove that the new lower bound is tighter than the Bayesian quantum Cramer-Rao bounds.
• Score: 21.22196305592545
• License: http://creativecommons.org/licenses/by/4.0/
• 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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