Stabilizer Entanglement Enhances Magic Injection
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908556185305088 |
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| author | Hou, Zong-Yue Cao, ChunJun Yang, Zhi-Cheng |
| author_facet | Hou, Zong-Yue Cao, ChunJun Yang, Zhi-Cheng |
| contents | 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 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 $U_A$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20873 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilizer Entanglement Enhances Magic Injection Hou, Zong-Yue Cao, ChunJun Yang, Zhi-Cheng Quantum Physics Statistical Mechanics 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 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 $U_A$. 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. |
| title | Stabilizer Entanglement Enhances Magic Injection |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2503.20873 |