Can NSI affect non-local correlations in neutrino oscillations?

Non-local correlations in entangled systems are usually captured by measures such as Bell's inequality violation. It was recently shown that in neutrino systems, a measure of non-local advantage of quantum coherence (NAQC) can be considered as a stronger measure of non-local correlations as compared to the Bell's inequality violation. In this work, we analyze the effects of non standard interaction (NSI) on these measures in the context of two flavour neutrino oscillations for DUNE, MINOS, T2K, KamLAND, JUNO and Daya Bay experimental set-ups. We find that even in the presence of NSI, Bell's inequality violation occurs in the entire energy range whereas the NAQC violation is observed only in some specific energy range justifying the more elementary feature of NAQC. Further, we find that NSI can enhance the violation of NAQC and Bell's inequality parameter in the higher energy range of a given experimental set-up; these enhancements being maximal for the KamLAND experiment. However, the possible enhancement in the violation of the Bell's inequality parameter over the standard model prediction can be up to 11% whereas for NAQC it is 7%. Thus although NAQC is a comparatively stronger witness of nonclassicality, it shows lesser sensitivity to NSI effects in comparison to the Bell's inequality parameter.