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

Suzuki, Jun

doi:10.1587/transfun.2023tap0014

IEICE Trans. Fundamentals

2024

DOI: 10.1587/transfun.2023tap0014

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

Jun Suzuki

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 tigh… Show more

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2024

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Cited by 2 publications

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First-principles construction of symmetry-informed quantum metrologies

Rubio

2024

Phys. Rev. A

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Combining quantum and Bayesian principles leads to optimality in metrology, but the optimization equations involved are often hard to solve. This Letter mitigates this problem with a class of measurement strategies for quantities isomorphic to location parameters, which are shown to admit a closed-form optimization. The resulting framework admits any parameter range, prior information, or state, and the associated estimators apply to finite samples. As an example, the metrology of relative weights is formulated from first principles and shown to require hyperbolic errors. The primary advantage of this approach lies in its simplifying power: it reduces the search for good strategies to identifying which symmetry leaves a state of maximum ignorance invariant. This will facilitate the application of quantum metrology to fundamental physics, where symmetries play a key role. Published by the American Physical Society 2024

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First-principles construction of symmetry-informed quantum metrologies

Rubio

2024

Phys. Rev. A

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Multiparameter Estimation with Two-Qubit Probes in Noisy Channels

Conlon

Lam

Assad

2023

Entropy

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This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka–Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.

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

Cited by 2 publications

References 36 publications

First-principles construction of symmetry-informed quantum metrologies

First-principles construction of symmetry-informed quantum metrologies

Multiparameter Estimation with Two-Qubit Probes in Noisy Channels

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