Probing Quantum Entanglement in ${\tau }^{+}{\tau }^{-}$ Pairs via the $\pi \pi$ Channel at STCF

Quantum entanglement and Bell-inequality violation in ${\tau }^{+}{\tau }^{-}$ pairs provide a sensitive probe of quantum correlations in high-energy interactions. We present a feasibility study of $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ at the proposed Super Tau-Charm Facility based on full Monte Carlo simulation at $\sqrt{s}=7$ GeV, focusing on the $\pi \pi$ channel (${\tau }^{\pm }\to {\pi }^{\pm }\nu$), which offers the maximal spin-analyzing power $\mathrm{\mid }\kappa \mathrm{\mid }=1$ and the simplest final-state topology for validating the quantum-tomography framework. We establish a consistency chain from the tree-level QED prediction through truth-level and detector-level reconstruction, yielding a reconstructed concurrence of $0.279\pm 0.007$ with the good-solution approach. A complementary full-simulation study of the $\rho \rho$ channel is also briefly reported. These results demonstrate that the STCF can provide a competitive platform for precision studies of quantum correlations in $\tau$-lepton pairs.