Quantum Information of Photon Pairs at Lepton Colliders

Photon pairs have provided an ideal laboratory for exploring entanglement and Bell inequality violation in low-energy experiments. Extending such studies to high-energy colliders is of great interest but has yet to be explored. Exploiting the photon conversion process for nearly on-shell photons, we formulate a factorization framework and an effective two-qubit description, which enable access to quantum information encoded in photon pairs. Using the existing Belle data set, we estimate that a $7.4\sigma$ violation of the Bell inequality could be achieved. The same framework can also probe quantum discord and nonstabilizerness, which could be measured with precisions of 5.6\% and 1.6\%, respectively. All the reconstructed results from photon conversion in the two-qubit framework are found to be consistent with the kinematic approach of real photons, and the formalism can apply to other spin-1 systems in an appropriate two-qubit limit.