A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement

doi:10.1109/JAS.2022.106079

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	A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement
	Yangyang Zhao; Fuyuan Xiao; Masayoshi Aritsugi; Weiping Ding
发表期刊	IEEE/CAA Journal of Automatica Sinica
ISSN	2329-9266
	2023
卷号	10 期号:2 页码:439-450
摘要	Fidelity plays an important role in quantum information processing, which provides a basic scale for comparing two quantum states. At present, one of the most commonly used fidelities is Uhlmann-Jozsa (U-J) fidelity. However, U-J fidelity needs to calculate the square root of the matrix, which is not trivial in the case of large or infinite density matrices. Moreover, U-J fidelity is a measure of overlap, which has limitations in some cases and cannot reflect the similarity between quantum states well. Therefore, a novel quantum fidelity measure called quantum Tanimoto coefficient (QTC) fidelity is proposed in this paper. Unlike other existing fidelities, QTC fidelity not only considers the overlap between quantum states, but also takes into account the separation between quantum states for the first time, which leads to a better performance of measure. Specifically, we discuss the properties of the proposed QTC fidelity. QTC fidelity is compared with some existing fidelities through specific examples, which reflects the effectiveness and advantages of QTC fidelity. In addition, based on the QTC fidelity, three discrimination coefficients ${\bm{d_1^{{\bf{QTC}}} }}$, ${\bm{d_2^{{\bf{QTC}}}}}$, and ${\bm{d_3^{{\bf{QTC}}}}}$ are defined to measure the difference between quantum states. It is proved that the discrimination coefficient ${\bm{d_3^{{\bf{QTC}}} }}$ is a true metric. Finally, we apply the proposed QTC fidelity-based discrimination coefficients to measure the entanglement of quantum states to show their practicability.
关键词	Distance measure entanglement measurement fidelity measure quantum Tanimoto coefficient (QTC) similarity measure uncertainty
DOI	10.1109/JAS.2022.106079
引用统计	被引频次：1[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/50857
专题	学术期刊_IEEE/CAA Journal of Automatica Sinica
推荐引用方式 GB/T 7714	Yangyang Zhao,Fuyuan Xiao,Masayoshi Aritsugi,et al. A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement[J]. IEEE/CAA Journal of Automatica Sinica,2023,10(2):439-450.
APA	Yangyang Zhao,Fuyuan Xiao,Masayoshi Aritsugi,&Weiping Ding.(2023).A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement.IEEE/CAA Journal of Automatica Sinica,10(2),439-450.
MLA	Yangyang Zhao,et al."A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement".IEEE/CAA Journal of Automatica Sinica 10.2(2023):439-450.

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