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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.08797 |
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| _version_ | 1866915829645312000 |
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| author | La Piana, Francesca |
| author_facet | La Piana, Francesca |
| contents | Recently De les Coves, Drescher and Netzer showed that an analogue of the Birkhoff--von Neumann theorem fails in the quantum setting. Motivated by this and questions arising in the study of quantum automorphisms of graphs, we introduce a graph-based variant of quantum magic squares and show that the analogue already fails for the cycle \(C_4\), via an explicit counterexample. We also show that they admit monic linear matrix inequality descriptions, hence form compact free spectrahedra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graph Quantum Magic Squares and Free Spectrahedra La Piana, Francesca Mathematical Physics Operator Algebras Recently De les Coves, Drescher and Netzer showed that an analogue of the Birkhoff--von Neumann theorem fails in the quantum setting. Motivated by this and questions arising in the study of quantum automorphisms of graphs, we introduce a graph-based variant of quantum magic squares and show that the analogue already fails for the cycle \(C_4\), via an explicit counterexample. We also show that they admit monic linear matrix inequality descriptions, hence form compact free spectrahedra. |
| title | Graph Quantum Magic Squares and Free Spectrahedra |
| topic | Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2512.08797 |