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Based on 10 billion $J/\psi$ events collected at the BESIII experiment, asearch for $CP$ violation in $\Lambda$ decay is performed in the differencebetween $CP$-odd decay parameters $\alpha_{-}$ for $\Lambda \rightarrow p\pi^-$and $\alpha_{+}$ for $\bar\Lambda \rightarrow \bar{p}\pi^+$ by using theprocess $e^+e^- \to J/\psi \rightarrow \Lambda \bar\Lambda $. With afive-dimensional fit to the full angular distributions of the daughter baryon,the most precise values for the decay parameters are determined to be$\alpha_{-} = 0.7519 \pm 0.0036 \pm 0.0024$ and $\alpha_{+} = -0.7559 \pm0.0036 \pm 0.0030$, respectively. The $\Lambda$ and $\bar{\Lambda}$ averagedvalue of the decay parameter is extracted to be $\alpha_{\rm{avg}} = 0.7542 \pm0.0010 \pm 0.0024$ with unprecedented accuracy. The $CP$ asymmetry$A_{CP}=(\alpha_{-}+\alpha_{+})/(\alpha_{-}-\alpha_{+})$ is determined to be$-0.0025 \pm 0.0046 \pm 0.0012$, which is one of the most precise measurementsin the baryon sector. The reported results for the decay parameter will play animportant role in the studies of the polarizations and $CP$ violations for thestrange, charmed and beauty baryons.

Precise Measurements of Decay Parameters and $CP$ Asymmetry with Entangled $\Lambda-\bar{\Lambda}$ Pairs