  Measurement-induced nonlocality (MiN), introduced by Luo and Fu [Phys. Rev.
Lett. 106(2011)120401], is a kind of quantum correlation that beyond
entanglement and even beyond quantum discord. Recently, we extended MiN to
infinite-dimensional bipartite system [arXiv:1107.0355]. MiN is defined over
one-sided projective measurements. In this letter we introduce a
measurement-induced nonlocality over two-sided projective measurements. The
nullity of this two-sided MiN is characterized, a formula for calculating
two-sided MiN for pure states is proposed, and a lower bound of (two-sided) MiN
for maximally entangled mixed states is given. In addition, we find that
(two-sided) MiN is not continuous. The two-sided geometric measure of quantum
discord (GMQD) is introduced in [Phys. Lett. A 376(2012)320--324]. We extend it
to infinite-dimensional system and then compare it with the two-sided MiN. Both
finite- and infinite-dimensional cases are considered.
