Prospects of measuring quantum entanglement in $\tau\tau$ final states at a future $e^+e^-$ Higgs factory

We introduce a method to study quantum entanglement at a future $e^+e^-$ Higgs factory (here the Future Circular Collider colliding $e^+$ and $e^-$ (FCC-ee) operating at $\sqrt{s}=240\,\mathrm{GeV}$) in the $\tau\tau$ final state. This method is focused on the $\tau \to \pi \nu_\tau$ decay. We show how the introduced method works on simulated events without detector effects. When detector effects are applied, the necessary $\tau$ four-momenta can be reconstructed from kinematic constraints. We will discuss the advantages of $e^+e^-$ collisions over $pp$ collisions where the reconstruction of the $\tau\tau$ rest frame is more difficult. This discussion will focus on the influence of $p_T$ trigger cuts on the visible $\pi^\pm$ in the $\tau$ lepton decay.