Multipartite Non-local Magic and SYK Model
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| Format: | Preprint |
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2026
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| _version_ | 1866914236328837120 |
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| author | Malvimat, Vinay Sarkis, Matthieu Suk, Yena Yoon, Junggi |
| author_facet | Malvimat, Vinay Sarkis, Matthieu Suk, Yena Yoon, Junggi |
| contents | We investigate the structure of quantum magic in interacting disordered fermionic systems, quantifying non-stabilizerness via the fermionic stabilizer Rényi entropy (SRE). To resolve the distribution of magic across different scales, we introduce a multipartite non-local magic functional, constructed from an inclusion-exclusion combination of subsystem contributions. This measure serves as a fine-grained diagnostic, isolating genuinely global contributions and revealing nontrivial interactions between local and collective supports of magic. We illustrate the measure on paradigmatic multipartite states and apply these diagnostics to the Sachdev-Ye-Kitaev model and its variants. Crucially, for thermal/typical ensembles, we observe a marked disparity between Thermal Pure Quantum (TPQ) states and the thermal density matrix. This reveals a concealed complexity: the immense computational hardness characterizing the unitary evolution is encoded in the specific microstructure of the black hole microstates, while being washed out in the coarse-grained thermodynamic description. Furthermore, in $\mathcal N=2$ supersymmetric SYK, we show that while fortuitous BPS states exhibit intermediate stabilizer complexity, the multipartite measure unveils a rich, sector-dependent pattern of global correlations, distinguishing them from generic chaotic states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_03076 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multipartite Non-local Magic and SYK Model Malvimat, Vinay Sarkis, Matthieu Suk, Yena Yoon, Junggi High Energy Physics - Theory Quantum Physics We investigate the structure of quantum magic in interacting disordered fermionic systems, quantifying non-stabilizerness via the fermionic stabilizer Rényi entropy (SRE). To resolve the distribution of magic across different scales, we introduce a multipartite non-local magic functional, constructed from an inclusion-exclusion combination of subsystem contributions. This measure serves as a fine-grained diagnostic, isolating genuinely global contributions and revealing nontrivial interactions between local and collective supports of magic. We illustrate the measure on paradigmatic multipartite states and apply these diagnostics to the Sachdev-Ye-Kitaev model and its variants. Crucially, for thermal/typical ensembles, we observe a marked disparity between Thermal Pure Quantum (TPQ) states and the thermal density matrix. This reveals a concealed complexity: the immense computational hardness characterizing the unitary evolution is encoded in the specific microstructure of the black hole microstates, while being washed out in the coarse-grained thermodynamic description. Furthermore, in $\mathcal N=2$ supersymmetric SYK, we show that while fortuitous BPS states exhibit intermediate stabilizer complexity, the multipartite measure unveils a rich, sector-dependent pattern of global correlations, distinguishing them from generic chaotic states. |
| title | Multipartite Non-local Magic and SYK Model |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2601.03076 |