Generality of the SEE–TCS correspondence beyond stabilizer codes

Determine whether the correspondence that links nontrivial subdimensional entanglement entropy (SEE) of a subdimensional entanglement subsystem to the existence of transparent composite symmetries (TCS)—where weak mixed-state symmetries act as transparent-patch operators of strong mixed-state symmetries—extends to quantum many-body systems outside Pauli stabilizer-code constructions, including generic interacting lattice models and non-stabilizer phases.

Background

The paper introduces subdimensional entanglement entropy (SEE) for lower-dimensional subsystems and shows that nontrivial SEE (nonzero subleading terms) is accompanied by a mixed-state symmetry structure termed transparent composite symmetry (TCS). In TCS, strong symmetries supported on the subsystem coexist with weak symmetries that act as transparent-patch operators of the strong ones, forming an algebra encoding a higher-dimensional topological order.

This correspondence is demonstrated explicitly in a range of stabilizer-code models (cluster states, toric codes, X-cube, Wen plaquette), where the reduced density matrices on the subdimensional entanglement subsystems exhibit strong-to-weak spontaneous symmetry breaking and robust TCS under finite-depth circuits. The open question is whether this SEE–TCS linkage persists in more general non-stabilizer settings.