\begin{document}$ e^+e^- $\end{document} colliders can improve the measurement accuracy of the spin correlation of tau lepton pairs from Higgs boson decay. We show the testability of Bell inequality through \begin{document}$ h{\rightarrow} \tau\tau $\end{document} at Circular Electron Positron Collider (CEPC). Two realistic methods of testing Bell inequality are investigated, i.e., Törnqvist's method and Clauser-Home-Shimony-Holt (CHSH) inequality. In the simulation, we consider the detector effects of CEPC including uncertainties for tracks and jets from Z boson in the production of \begin{document}$ e^+e^-{\rightarrow} Zh $\end{document}. Necessary reconstruction approaches are described to measure quantum entanglement between \begin{document}$ \tau^+ $\end{document} and \begin{document}$ \tau^- $\end{document}. Finally, we show the sensitivity of CEPC to Bell inequality violation for the two methods."> Testing Bell inequality through <inline-formula><tex-math id="M1">\begin{document}${\boldsymbol h{\bf\rightarrow}\boldsymbol\tau\boldsymbol\tau }$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/cd28c9a9-0f07-42fb-a76a-683204bf39f6/CPC-2024-0071_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/cd28c9a9-0f07-42fb-a76a-683204bf39f6/CPC-2024-0071_M1.png"/></alternatives></inline-formula> at CEPC -
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