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Bayesian Logarithmic Derivative Type Lower Bounds for Quantum Estimation

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arxiv 2405.10525 v2 pith:L3WXL7H5 submitted 2024-05-17 quant-ph

Jianchao Zhang , Jun Suzuki This is my paper · ORCID
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keywords bayesianlowerboundboundsestimationquantumapproachderivative
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Measurement incompatibility in Bayesian multiparameter quantum estimation

    quant-ph 2025-11 accept novelty 7.0 of 10

    Measurement incompatibility at most doubles the minimum mean-square loss in Bayesian multiparameter quantum estimation, relative to the symmetric-posterior-mean bound.

  2. Multiparameter quantum estimation with Gaussian states: efficiently evaluating Holevo, RLD and SLD Cram\'er-Rao bounds

    quant-ph 2025-04 conditional novelty 7.0 of 10

    A semidefinite program over quadratic phase-space observables computes the Holevo Cramér-Rao bound for Gaussian states with parameters encoded in both the first moments and the covariance matrix.

  3. Hybrid Cram\'er-Rao bound for Quantum Bayes-Point Estimation with Nuisance Parameters

    quant-ph 2025-10 conditional novelty 6.0 of 10

    A prior-averaged hybrid quantum Fisher information matrix is defined, and a Cramér-Rao bound on the mean-squared error of fixed interest parameters with random nuisance parameters is proven.

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