From Longman Dictionary of Contemporary Englishwave a magic wandwave a magic wandto make a bad situation better, even though this is impossible I can’t wave a magic wand and change what happened. → wave
Examples from the Corpus
wave a magic wand• I ask, if you could wave a magic wand, what would your life look like?• If that is true, he is waving a magic wand with a sledgehammer on the end. 