L$\ddot {u}$der Rule, Von Neumann Rule and Cirelson’s Bound of Bell CHSH Inequality

In [PRL, 113, 050401 (2014)] the authors have shown that instead of L$\ddot{u}$der rule, if degeneracy breaking von Neumann projection rule is adopted for state reduction, quantum value three-time Leggett-Garg inequality can exceed it's L$\ddot{u}$ders bound. Such violation bound may even approach algebraic maximum in asymptotic limit system size. They also claim Clauser-Horne-Shimony-Holt (CHSH) such (known as Cirelson's bound) cannot be obtained when measurement performed sequentially first by Alice followed Bob. this paper, we used, CHSH exceeds and reach its four. This thus provide a strong objection regarding viability valid reduction rule. Further, pointed out occurs due to injection additional non-locality act implementing