  In the present paper, we attempt to address the question of "can tensorizing
states have quantum advantages?". To answer this question, we exploit the
notion of measurement-induced nonlocality (MIN) and advocate a fidelity based
nonbilocal measure to capture the nonlocal effects of tensorizing states due to
locally invariant von Neumann projective measurements. We show that the
properties of the fidelity based nonbilocal measure are retrieved from that of
MIN. Analytically, we evaluate the nonbilocal measure for any arbitrary pure
state. The upper bounds of the nonbilocal measure based on fidelity are also
obtained in terms of eigenvalues of correlation matrix. As an illustration, we
have computed the nonbilocality for some popular input states.
