Stabilizer Entanglement as a Magic Highway

Zong-Yue Hou, ChunJun Cao, Zhi-Cheng Yang (Mar 28 2025).

Abstract: Non-stabilizerness is a key resource for fault-tolerant quantum computation, yet its interplay with entanglement in dynamical settings remains underexplored. We study a well-controlled, analytically tractable setup that isolates entanglement generation from magic injection. We analytically and numerically demonstrate that stabilizer entanglement functions as a highway that facilitates the spreading of locally injected magic throughout the entire system. Specifically, for an initial stabilizer state with bipartite entanglement $E$, the total magic growth, quantified by the linear stabilizer entropy $Y$, follows $\overline{Y}\propto 2^{-|A|-E}$ under a Haar random unitary on a local subregion $A$. Moreover, when applying a tensor product of local Haar random unitaries, the resulting state's global magic approaches that of a genuine Haar random state if the initial stabilizer state is sufficiently entangled by a system-size-independent amount. Similar results are also obtained for tripartite stabilizer entanglement. We further extend our analysis to non-stabilizer entanglement and magic injection via a shallow-depth brickwork circuit, and find that the qualitative picture of our conclusion remains unchanged.

Arxiv: https://arxiv.org/abs/2503.20873