New observables for testing Bell inequalities in $W$ boson pair production

We show that testing Bell inequalities in $W^\pm$ pair systems by measuring their angular correlation suffers from the ambiguity in kinetical reconstruction of the di-lepton decay mode. We further propose a new set of Bell observables based on the measurement of the linear polarization of the $W$ bosons, providing a realistic observable to test Bell inequalities in $W^\pm$ pair systems for the first time.