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.
RT @docmilanfar Random matrices (e.g. Wigner, Wishart, Widom) are very important in modern statistics and learning - A model about which much less is known is uniformly sampled matrices from the set of doubly stochastic matrices: Uniformly Distributed Stochastic Matrices A short thread 1/n
A new criterion for quantum channel incompatibility, based on Fisher information. Joint work with Qing-Hua Zhang scirate.com/arxiv/2204.099… . The core idea is to use a criterion for measurement incompatibility derived by H. Zhu, and use it for associated POVMs. pic.twitter.com/AQ59UmE3NV