  Geometrical methods in quantum information are very promising for both
providing technical tools and intuition into difficult control or optimization
problems. Moreover, they are of fundamental importance in connecting pure
geometrical theories, like GR, to quantum mechanics, like in the AdS/CFT
correspondence. In this paper, we first make a survey of the most important
settings in which geometrical methods have proven useful to quantum information
theory. Then, we lay down a general framework for an action principle for
quantum resources like entanglement, coherence, and anti-flatness. We discuss
the case of a two-qubit system.
