Fidelity Strange Correlators for Average Symmetry-Protected Topological Phases

Abstract

Topological phases in open quantum systems have become an exciting area of research, driven by the rising importance of noisy intermediate-scale quantum platforms. The concept of Average Symmetry-Protected Topological (ASPT) phases extends symmetry-protected topological phases to quantum systems affected by disorder or decoherence. To identify nontrivial ASPT states, we introduce a "fidelity strange correlator" (FSC), which operates directly on a single bulk density matrix without boundaries. For nontrivial ASPT phases in one and two dimensions, we show that the FSC reveals long-range or power-law behavior. In several two-dimensional examples, we establish a link between the FSC and certain non-local correlation functions in statistical loop models with quantum corrections, enabling us to derive exact scaling exponents for the FSC. In addition, we discuss methods to measure the FSC using classical shadow tomography. Our work lays the groundwork for identifying these intriguing topological phases of matter in open quantum systems, both numerically and experimentally.