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
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.
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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