Observation of quantum entanglement in $\Lambda \bar{\Lambda }$ pair production via electron-positron annihilation

Abstract

We report the observation of quantum entanglement in $\Lambda \bar{\Lambda }$ pairs produced via electron-positron annihilation, specifically through the decay $J/\psi \to \Lambda \bar{\Lambda }$. By analyzing the angular correlations of the subsequent weak decays $\Lambda \to p{\pi }^{-}$ and $\bar{\Lambda }\to \bar{p}{\pi }^{+}$, we derive normalized observables ${\mathcal{O}}_i(i=0,1,\dots ,4)$ that distinguish entangled states from separable ones. Theoretical predictions for these observables are established, with violations of separable-state bounds serving as unambiguous signatures of entanglement. Experimental measurements at $\cos {\theta }_{\Lambda }=0$ yield ${\mathcal{O}}_{1\text{min}}^{\text{Observed}}=-0.7374\pm 0.0011\pm 0.0016$, significantly exceeding the classical limit of $-0.5$ with a statistical significance of 124.9$\sigma$. For $\left|\cos {\theta }_{\Lambda }\right|<0.4883$, the observed ${\mathcal{O}}_1^{\text{Observed}}$ consistently exhibits ${\mathcal{O}}_1^{\text{Observed}}<-\frac{1}{2}$ with a statistical significance of at least 5$\sigma$. Since $69.3\%$ of the decay events involving $\Lambda \to p+{\pi }^{-}$ and $\bar{\Lambda }\to \bar{p}+{\pi }^{+}$ are spacelike-separated, our results confirming the persistence of quantum entanglement in the $\Lambda \bar{\Lambda }$ system provide strong support for the non-locality of quantum mechanics. The findings are consistent with theoretical expectations under decoherence-free conditions, highlighting the potential of hyperon pairs as probes for fundamental quantum phenomena.

Comments: 15 pages, 2 figures