This talk follows some of the problems originating in Vern Paulsen's work and related results, starting from optimization problems in frame theory and transitioning to questions in quantum information theory. Examples include the design of frames as codes in order to mitigate the effect of data loss in classical transmissions, as well as to suppress the effect of decoherence in quantum channels. A related design problem is whether an orthogonal projection that has nearly constant diagonal is close to one whose diagonal is constant. Finally, the construction of a maximal set of equiangular lines in any complex finite-dimensional Hilbert space is related to entanglement breaking properties of a one-parameter family of quantum channels.