首页|Holevo bound independent of weight matrices for estimating two parameters of a qubit

Holevo bound independent of weight matrices for estimating two parameters of a qubit

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Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estima-tions,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,with-out 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 pre-cisions 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.

quantum metrologyquantum Fisher informationHolevo boundquantum multi-parameter esti-mation

牛畅、郁司夏

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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

Hefei National Laboratory,University of Science and Technology of China,Hefei 230088,China

Key-Area Research and Development Program of Guangdong Province of ChinaKey-Area Research and Development Program of Guangdong Province of China

2020B0303010001SIQSE202104

2024

10.1088/1674-1056/ad117d

中国物理B(英文版)
中国物理学会和中国科学院物理研究所

中国物理B(英文版)

CSTPCDEI
影响因子：0.995
ISSN：1674-1056
年,卷(期)：2024.33(2)
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