After recalling basic facts from quantum information theory (density matrices, partial trace, purification), I’ll present two examples of random states: the induced Gaussian state and the uniform pure one on the Euclidean sphere. Afterwards, I’ll introduce the dynamical version of the latter which leads to the problem of computing the joint law of the moduli of a given set of its coordinates. The first approach to solve this problem is based on solving a heat equation in the simplex but lacks the knowledge of boundary conditions and a natural choice of basis. The second approach is rather based on direct computations by means of unitary spherical harmonics and gives rise to the so-called Jacobi polynomials in the simplex.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
