Abstract
Measurement-induced nonlocality is a measure of nonlocality introduced recently by Luo and Fu. We present here sufficient and necessary conditions for a quantum state for which this quantity is equal to zero. Furthermore it is shown that for such a state ρab with any local channel acting on Ha cannot create measurement-induced nonlocality if and only if either it is a completely contractive channel or it is a nontrivial isotropic channel. For the qubit case this property is an additional characteristic of the completely contractive channel or the commutativity-preserving unital channel.
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