We propose an experimental test of local hidden variable theories against quantum mechanics by measuring the polarization correlation of entangled vector meson pairs. The form of correlation is reproduced by treating the decay of a phi meson as the measurement to its polarization vector. This interpretation is straightforward and provide more detailed information on the quantum entanglement in high energy physics. Such a test can be carried out at BESIII and the data analysis is ongoing. The estimation of background level is essential for this analysis. We provided a proper description of the reconstructed mass spectrum of eta_c so that the fraction of backgrounds events can be estimated more preciously.