Limit formulas for the trace of the functional calculus of quantum channels for $SU(2)$

TL;DR

This paper generalizes limit formulas for traces of quantum channels related to $SU(2)$, connecting them with Berezin transforms and extending previous Wehrl-type inequalities.

Contribution

It introduces new quantum channels for all tensor product components of $SU(2)$ representations and generalizes existing limit formulas.

Findings

Established limit formulas using Berezin transforms.

Extended Wehrl-type inequalities to new quantum channels.

Connected trace limits with functional calculus of quantum channels.

Abstract

Lieb and Solovej \cite{liebsolBloch} 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. 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.