Bayesian Logarithmic Derivative Type Lower Bounds for Quantum Estimation

• URL: http://arxiv.org/abs/2405.10525v2
• Date: Fri, 23 Aug 2024 14:09:44 GMT
• Title: Bayesian Logarithmic Derivative Type Lower Bounds for Quantum Estimation
• Authors: Jianchao Zhang, Jun Suzuki,
• Abstract summary: Recently, a lower bound, called the Bayesian Nagaoka-Hayashi bound for the Bayes risk in quantum domain was proposed. This paper is to explore this Bayesian Nagaoka-Hayashi bound further by obtaining its lower bounds.
• Score: 17.305295658536828
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian approach for quantum parameter estimation has gained a renewed interest from practical applications of quantum estimation theory. Recently, a lower bound, called the Bayesian Nagaoka-Hayashi bound for the Bayes risk in quantum domain was proposed, which is an extension of a new approach to point estimation of quantum states by Conlon et al. (2021). The objective of this paper is to explore this Bayesian Nagaoka-Hayashi bound further by obtaining its lower bounds. We first obtain one-parameter family of lower bounds, which is an analogue of the Holevo bound in point estimation. Thereby, we derive one-parameter family of Bayesian logarithmic derivative type lower bounds in a closed form for the parameter independent weight matrix setting. This new bound includes previously known Bayesian lower bounds as special cases.

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