Effect of Off-diagonal NSI Parameters on Entanglement Measurements in Neutrino Oscillations

In this work, we explore the influence of off-diagonal non-standard interaction (NSI) parameters on quantum entanglement within the three-flavor neutrino oscillation framework. By expressing three key entanglement measures: Entanglement of Formation (EOF), Concurrence, and Negativity in terms of oscillation probabilities, we analyze how these quantum correlations are affected by the NSI parameters $\epsilon_{e\mu}$, $\epsilon_{e\tau}$, and $\epsilon_{\mu\tau}$, including their complex phases. The quantum correlation measures considered in this work cannot be extracted directly from event rates, but solely in terms of oscillation probabilities. Using the DUNE experiment as a reference point, our analysis shows that NSI effects are most pronounced at lower energies, while Negativity continuing to dominate even at higher energies. It is observed that $\epsilon_{e \mu}$ and $\epsilon_{e \tau}$ affect entanglement measures mainly through the appearance channel, while the impact of $\epsilon_{\mu \tau}$ on EOF, Concurrence, and Negativity is predominantly linked to the disappearance channel. Further, our results show that Negativity is more sensitive than EOF and Concurrence in the [Energy ($E$) - $\delta_{CP}$] plane under the influence of off-diagonal NSI scenarios, displaying a clear dependence of the CP-violating phase, $\delta_{CP}$ on specific energy ranges, particularly in the lower energy regime.