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Holevo bound independent of weight matrices for estimating two parameters of a qubit |
| Chang Niu(牛畅)1 and Sixia Yu(郁司夏)1,2,† |
1 Department of Modern Physics & Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China;
2 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China |
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Abstract Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations, which can be asymptotically achieved. Except for some trivial cases, the Holevo bound is implicitly defined and formulated with the help of weight matrices. Here we report the first instance of an intrinsic Holevo bound, namely, without any reference to weight matrices, in a nontrivial case. Specifically, we prove that the Holevo bound for estimating two parameters of a qubit is equivalent to the joint constraint imposed by two quantum Cramér-Rao bounds corresponding to symmetric and right logarithmic derivatives. This weightless form of Holevo bound enables us to determine the precise range of independent entries of the mean-square error matrix, i.e., two variances and one covariance that quantify the precisions of the estimation, as illustrated by different estimation models. Our result sheds some new light on the relations between the Holevo bound and quantum Cramér-Rao bounds. Possible generalizations are discussed.
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Received: 16 November 2023
Revised: 30 November 2023
Accepted manuscript online: 01 December 2023
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PACS:
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03.65.-w
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(Quantum mechanics)
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03.65.Aa
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(Quantum systems with finite Hilbert space)
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03.65.Ta
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(Foundations of quantum mechanics; measurement theory)
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03.67.-a
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(Quantum information)
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| Fund: Project supported by the Key-Area Research and Development Program of Guangdong Province of China (Grant Nos. 2020B0303010001 and SIQSE202104). |
Corresponding Authors:
Sixia Yu
E-mail: yusixia@ustc.edu.cn
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Cite this article:
Chang Niu(牛畅) and Sixia Yu(郁司夏) Holevo bound independent of weight matrices for estimating two parameters of a qubit 2024 Chin. Phys. B 33 020304
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