  Kubo's canonical correlation functions (canonical correlators) describe the
static response of a system in equilibrium to infinitesimal local
perturbations. Knowing their decay properties with respect to spatial distance
is important for many theoretical and experimental applications. For a thermal
state of a system with short-range interactions, we prove that any knowledge of
the decay rate of ordinary correlators readily translates into that of
canonical correlators. As the former have been extensively studied, our result
can lead to many new results on the latter. Throughout the paper, we use the
framework of infinite-volume quantum lattice model. However, the method we use
is adaptable for other physical scenarios not considered in this paper.
