Stabilizer R'enyi moments beyond entanglement

Stabilizer Rényi moments depend on a choice of operator basis and need not be determined by entanglement spectra. In this paper, we study their spatial decay in critical quantum chains described by two-dimensional conformal field theories. We derive an exact entanglement baseline for reductions of pure stabilizer states and a symmetry selection rule for the charged contribution at fixed support. An exact Ising example shows that an on-site rotation changes the full decay exponent while preserving every subsystem entanglement spectrum. For growing Ising intervals at index two, we obtain an exact Pfaffian representation and compare the charged amplitude with a candidate conformal boundary calculation. The data support this prediction, but its identification with the lattice limit still requires endpoint matching and control of the order of limits.