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arXiv · 2503.20873

Stabilizer Entanglement Enhances Magic Injection

Zong-Yue Hou·ChunJun Cao·Zhi-Cheng Yang
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Abstract

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 $U_A$ is applied to a subsystem $A$ of an entangled stabilizer state, the total injected magic increases with the entanglement between $A$ and its complement. More generally, for any unitary $U_A$, 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 R\'enyi 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 $U_A$. 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.

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Zong-Yue Hou, ChunJun Cao, Zhi-Cheng Yang. 2025-03-26. Stabilizer Entanglement Enhances Magic Injection. https://doi.org/10.1038/s41534-026-01265-4

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