Appears in collection : 2017 - T3 - WS2 - Probabilistic techniques and quantum information theory

de Finetti theorems are pervasive in finite-dimensional quantum information theory as they state that permutation invariant quantum systems are in some sense close to convex mixtures of i. i. d. states. In this work, I’ll consider infinite-dimensional quantum systems that are invariant under a larger symmetry group, namely the unitary group U(n), and show that such states are similarly well approximated by convex mixtures of Gaussian i. i. d. states. I’ll then discuss how to apply this result to study truncations of random Haar unitary matrices. This talk is based on arXiv:1612. 05080.