  Average symmetry-protected topological (ASPT) phase is a generalization of
symmetry-protected topological phases to disordered systems or open quantum
systems. We devise a "strange correlator" in one and two dimensions to detect
nontrivial ASPT states. We demonstrate that for a nontrivial ASPT phase this
strange correlator exhibits long-range or power-law behavior. We explore the
connection between the strange correlators and correlation functions in
two-dimensional loop models with quantum corrections, leading to the exact
scaling exponents of the strange correlators.
