Measurement-Induced Entanglement in Subsystem-Symmetry-Protected Topological Phases

Subsystem-symmetry-protected topological (SSPT) phases feature many-body entangled states characterized by invariant symmetry action on lower-dimensional subsystems in 2D or 3D. Nontrivial phases are known for their utility in measurement-based quantum computing (MBQC). For example, the Z2×Z2 SSPT phase containing the 2D cluster state features computationally universal resources. A necessary property for MBQC resources is that local measurements may create long-ranged correlations. This measurement-induced entanglement (MIE) is a more general many-body phenomenon of recent interest. Tripartite MIE has been linked to computational advantage of quantum circuits in two dimensions. This raises the question of whether MIE plays a more general role in understanding SSPT phases and their utility. We propose operationally meaningful quantities in SSPT phases and discuss how MIE features in those SSPT phases.