BROOKLYN QUANTUM FRAMED

After a momentary hiatus, BQM returns in full force! This week we'll be picking up on some themes we last explored in our session of QBism. First: a gentle introduction to "frame theory." Frames provide a much more flexible notion of a coordinate system than the usual orthonormal bases. We'll study the simplest case of two real dimensions thoroughly to gain intuition (with some cool visualizations), and compare and contrast general frames with tight frames, unit norm tight frames, and equiangular frames. We'll then discuss the relationship between tight frames and rank-1 POVM's, and how, if a POVM has a sufficient number of elements, we can use it as an operator basis: in the quantum context, this allows us to place pure states and density matrices on an equal footing, and characterize both in terms of the probabilities for a single experiment. Finally, we'll allude to the some of the interesting differences that arise when one tries to play the game of quantum mechanics in real vs complex vector spaces.