Given a maximal orthogonal resolution of the identity B in the Hilbert space of a quantum system we define a measure of the coherence generating power of a unital operation with respect to B. This measure is the average coherence generated by the operation acting on an input ensemble of B-diagonal states. We give its explicit analytical form in any dimension andprovide an operational protocol to directly detect it. We characterize the set of unitaries with maximal coherence generating power and study the properties of our measure when the unitary is drawn at random from the Haar distribution. I will conclude by establishing a connection between this formalism and the Hilbert-Schmidt geometry of maximal abelian algebras of operators and its application to eigenstate phase transitions in interacting quantum systems e.g., many-body localization.
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