  We define the coherence non-activating measurement as the positive
operator-valued measurement which gives the same result whether or not the
coherence in a quantum state is destroyed. A connection is built between the
coherence activating ability of a measurement and its ability to steer quantum
states when coherence non-activating measurement is free. Then we study the
quantum discord based on coherence non-activating measurement and its behavior
under local incoherent operations. Our results contribute to the study of
resource non-activating condition, which is a complementary to the well-studied
resource non-generating condition.
