Entanglement-sensitive observables in $e^+e^- \to τ^+τ^-$ at STCF: a detector-level feasibility study
Quantum entanglement in $τ^+τ^-$ production provides a direct probe of non-classical spin correlations in a relativistic quantum system, with the $τ$ decay products serving as spin analyzers. We investigate the detector-level feasibility of such measurements in $e^+e^-\toτ^+τ^-$ at the Super Tau-Charm Facility (STCF) at $\sqrt{s}=7$ GeV, using the $ρρ$ and $πρ$ 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 $4.5\%$ and $4.8\%$, with corresponding purities of about $87.6\%$ and $93.2\%$ for the $ρρ$ and $πρ$ channels, respectively. From the reconstructed decay kinematics, the $τ^+τ^-$ spin-density matrix is inferred and the concurrence $C[ρ]$ together with the Bell-sensitive quantity $m_{12}[C]$ are evaluated in a selected fiducial region. For the benchmark requirement $|\cosθ|<0.2$ and an integrated luminosity of $1~\mathrm{ab}^{-1}$, the projected relative precision on $C[ρ]$ is about $2.2\%$ in both channels, while that on $m_{12}[C]$ is approximately $1.4\%$ for $ρρ$ and $1.5\%$ for $πρ$, including statistical and detector-resolution uncertainties. The reconstructed $m_{12}[C]$ shows a larger separation from its reference threshold in the $ρρ$ 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 $τ$ decays at STCF.