Bayesian Logarithmic Derivative Type Lower Bounds for Quantum Estimation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916366992277504 |
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| author | Zhang, Jianchao Suzuki, Jun |
| author_facet | Zhang, Jianchao Suzuki, Jun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10525 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bayesian Logarithmic Derivative Type Lower Bounds for Quantum Estimation Zhang, Jianchao Suzuki, Jun Quantum Physics 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. |
| title | Bayesian Logarithmic Derivative Type Lower Bounds for Quantum Estimation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.10525 |