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We present an information geometric characterization of quantum drivingschemes specified by su(2;C) time-dependent Hamiltonians in terms of bothcomplexity and efficiency concepts. By employing a minimum action principle,the optimum path connecting initial and final states on the manifold infinite-time is the geodesic path between the two states. In particular, thetotal entropy production that occurs during the transfer is minimized alongthese optimum paths. For each optimum path that emerges from the given quantumdriving scheme, we evaluate the so-called information geometric complexity(IGC) and our newly proposed measure of entropic efficiency constructed interms of the constant entropy production rates that specify the entropyminimizing paths being compared. From our analytical estimates of complexityand efficiency, we provide a relative ranking among the driving schemes beinginvestigated. Finally, we conclude by commenting on the fact that an higherentropic speed in quantum transfer processes seems to necessarily go along witha lower entropic efficiency together with a higher information geometriccomplexity.

Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions