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.
@roger_mansuy @AurelienAlvarez @ENSdeLyon @ENS_ULM @ImagesDesMaths A voir aussi les excellentes vidéos de @3blue1brown youtu.be/HEfHFsfGXjs et le lien entre ce problème et un algorithme quantique arxiv.org/abs/1912.02207
New paper with Satvik Singh on integrals over the diagonal unitary group and applications to quantum information scirate.com/arxiv/2007.112… . Stay tuned for the follow-up work on covariant channels, using the same diagrammatic calculus