Last week, at the invitation of Hun Hee Lee, I gave a series of three lectures on some applications of random matrix theory to problems in quantum information theory. The notes are available here. After discussing the Marchenko–Pastur theorem, I present my result with Teo Banica on partial transposition of random quantum states; this is also the occasion to review some basic facts from free probability. The third lecture dealt with random quantum channels, and I covered the results I obtained with Serban Belinschi and Benoit Collins here and here.
New paper out with @hippoquantus and Anna Jenčová on different characterizations of measurement compatibility in general probabilistic theories arxiv.org/abs/2011.06497 featuring tensor product of cones, tensor norms, as well as a generalization of spectrahedra pic.twitter.com/j0NBbCT8H2
RT @_____satvik In this new paper with @nechita_ion, we show that the PPT^2 conjecture holds for all Choi-type channels (and more), thus exhibiting the unsuitablity of a large class of states from the perspective of repeater protocols. scirate.com/arxiv/2011.038…