Analysis and Probability Seminar

Lieb and Solovej (2014) studied traces of quantum channels, defined by the leading component in the decomposition of the tensor product of two irreducible representations of $SU(2)$, to establish a Wehrl-type inequality for integrals of convex functions of matrix coefficients. It is proved that the integral is the limit of the trace of the functional calculus of quantum channels. I introduce new quantum channels for all the components in the tensor product and generalize their limit formula. I prove that the limit can be expressed using Berezin transforms.