Measurement-induced nonlocality based on the relative entropy

We quantify the measurement-induced nonlocality (Luo and Fu, Phys. Rev. Lett. 106, 1020401, 2011) from the perspective of the relative entropy. This quantification leads to an operational interpretation for the measurement-induced 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 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.