Quantum information and CP measurement in H plus -at future lepton colliders

We introduce a methodology and investigate the feasibility of measuring quantum properties of tau lepton pairs in the H -> tau+tau- decay at future lepton colliders. In particular, observation of entanglement, steerability, and violation of Bell inequalities are examined for the International Linear Collider (ILC) and Future Circular e+e- Collider (FCC-ee). We find that detecting quantum correlation crucially relies on precise reconstruction of the tau lepton rest frame, and a simple kinematics reconstruction does not suffice due to the finite energy resolution of the colliding beams and detectors. To correct for energy mismeasurements, a log-likelihood method is developed that incorporates the information of impact parameters of tau lepton decays. We demonstrate that an accurate measurement of quantum properties is possible with this method. As a by-product, we show that a novel model-independent test of CP violation can be performed and the CP phase of H tau tau interaction can be constrained with an accuracy comparable to dedicated analyses, i.e., up to 7.9 degrees and 5.4 degrees at ILC and FCC-ee, respectively.