Stabilizer entanglement enhances magic injection

Non-stabilizerness is a key resource for fault-tolerant quantum computation, yet its interplay with entanglement in dynamical settings remains underexplored. We address this by analyzing a well-controlled, analytically tractable setup, where we show that entanglement acts as a conduit that teleports magic across the system, thereby enhancing magic injection. Using exact calculations, we prove that when a Haar-random unitary UA is applied to a subsystem A of an entangled stabilizer state, the total injected magic increases with the amount of entanglement between A and its complement. More generally, for any unitary UA, we show that this enhancement is maximized when A is maximally entangled with its complement, in which case the total injected magic is exactly given by the unitary stabilizer Rényi entropy we introduce. This quantity provides both a directly computable measure of unitary magic and a lower bound on the minimum number of T gates required to synthesize UA. In particular, we show that the linear unitary stabilizer entropy gives a better estimate for the nonstabilizer content produced by UA than the previously proposed notion of nonstabilizing power. We further extend our analysis to tripartite stabilizer entanglement, non-stabilizer entanglement, and magic injection via shallow-depth brickwork circuits, finding that the qualitative picture remains unchanged.