Entanglement-sensitive observables in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ at STCF: a detector-level feasibility study

Quantum entanglement in ${\tau }^{+}{\tau }^{-}$ production provides a direct probe of non-classical spin correlations in a relativistic quantum system, with the $\tau$ decay products serving as spin analyzers. We investigate the detector-level feasibility of such measurements in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ at the Super Tau-Charm Facility (STCF) at $\sqrt{s}=7$ GeV, using the $\rho \rho$ and $\pi \rho$ decay channels. Signal and dominant background processes are simulated with the full STCF detector and reconstruction framework. Dedicated reconstruction and event-selection procedures yield overall signal efficiencies of approximately $4.5\mathrm{\%}$ and $4.8\mathrm{\%}$, with corresponding purities of about $87.6\mathrm{\%}$ and $93.2\mathrm{\%}$ for the $\rho \rho$ and $\pi \rho$ channels, respectively. From the reconstructed decay kinematics, the ${\tau }^{+}{\tau }^{-}$ spin-density matrix is inferred and the concurrence $C[\rho ]$ together with the Bell-sensitive quantity $m_{12}[C]$ are evaluated in a selected fiducial region. For the benchmark requirement $\mathrm{\mid }\cos \theta \mathrm{\mid }<0.2$ and an integrated luminosity of $1{\mathrm{a}\mathrm{b}}^{-1}$, the projected relative precision on $C[\rho ]$ is about $2.2\mathrm{\%}$ in both channels, while that on $m_{12}[C]$ is approximately $1.4\mathrm{\%}$ for $\rho \rho$ and $1.5\mathrm{\%}$ for $\pi \rho$, including statistical and detector-resolution uncertainties. The reconstructed $m_{12}[C]$ shows a larger separation from its reference threshold in the $\rho \rho$ channel, making this topology particularly sensitive to Bell-type spin correlations. These results demonstrate the detector-level feasibility of probing quantum entanglement and non-classical spin correlations in hadronic $\tau$ decays at STCF.