In quantiki website (https://www.quantiki.org/wiki/bell-state) it is mentioned that verification of quantum correlation in rotated basis states is more important for quantum correlation. I also found in the paper "Malte C Tichy et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 192001" that "A SSR (superselection rule) that prevents a local basis rotation, e.g., may enforce that the entanglement which is formally present in a state effectively reduces to a classical correlation."
From these statements can I conclude that change of measurement basis somehow differentiate classical and quantum correlation.