Limit Formulas for the Trace of the Functional Calculus of Quantum Channels for SU(2)

Journal article, 2024

In 2014 Lieb and Solovej studied traces of quantum channels, which are 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. In this paper, we introduce new quantum channels for all the components in the tensor product and generalize their limit formula. We prove that the limit can be expressed using Berezin transforms.