  We quantify the measurement-induced nonlocality [Luo and Fu, Phys. Rev. Lett.
106, 120401 (2011)] from the perspective of the relative entropy. This
quantification leads to an operational interpretation for the
measurementinduced nonlocality, namely, it is the maximal entropy increase
after the locally invariant measurements. The relative entropy of nonlocality
is upper bounded by the entropy of the measured subsystem. We establish a
relationship between the relative entropy of nonlocality and the geometric
nonlocality based on the Hilbert- Schmidt norm, and show that it is equal to
the maximal distillable entanglement. Several trade-off relations are obtained
for tripartite pure states. We also give explicit expressions for the relative
entropy of nonlocality for Bell-diagonal states.
