A Quantum Tanimoto Coefficient Fidelity for Entanglement Measurement |
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| Y. Y. Zhao, F. Y. Xiao, M. Aritsugi, and W. P. Ding, “A quantum Tanimoto coefficient fidelity for entanglement measurement,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 439–450, Feb. 2023. doi: 10.1109/JAS.2022.106079 |
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| Authors: | Yangyang Zhao Fuyuan Xiao Masayoshi Aritsugi Weiping Ding |
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| Affiliation: | 1. School of Big Data and Software Engineering, Chongqing University, Chongqing 401331, China;2. Faculty of Advanced Science and Technology, Kumamoto University, Kumamoto 860-8555, Japan;3. School of Information and Technology, Nantong University, Nantong 223019, China |
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| Abstract: | 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 begin{document}${boldsymbol{d_1^{{bf{QTC}}} }}$end{document}![]() ![]() , begin{document}${boldsymbol{d_2^{{bf{QTC}}}}}$end{document}![]() ![]() , and begin{document}${boldsymbol{d_3^{{bf{QTC}}}}}$end{document}![]() ![]() are defined to measure the difference between quantum states. It is proved that the discrimination coefficient begin{document}${boldsymbol{d_3^{{bf{QTC}}} }}$end{document}![]() ![]() 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. |
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| Keywords: | Distance measure entanglement measurement fidelity measure quantum Tanimoto coefficient (QTC) similarity measure uncertainty |
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