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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.19857 |
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| _version_ | 1866913086551621632 |
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| author | de Jesus, Matheus R. Hoefel, Eduardo O. C. Angelo, Renato M. |
| author_facet | de Jesus, Matheus R. Hoefel, Eduardo O. C. Angelo, Renato M. |
| contents | Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric exchange properties. Here we establish a precise correspondence between graph topology and exchange symmetry by proving that a graph state is fully symmetric under particle permutations if and only if the underlying graph is complete. We then introduce a generalized graph-based construction using a non-commutative two-qudit gate, denoted $GR$, which requires directed edges and an explicit vertex ordering. We show that complete directed graphs generate fully antisymmetric multipartite states when endowed with appropriate orientations. Together, these results provide a unified graph-theoretic description of bosonic and fermionic exchange symmetry based on graph completeness and edge orientation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19857 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetric and Antisymmetric Quantum States from Graph Structure and Orientation de Jesus, Matheus R. Hoefel, Eduardo O. C. Angelo, Renato M. Quantum Physics Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric exchange properties. Here we establish a precise correspondence between graph topology and exchange symmetry by proving that a graph state is fully symmetric under particle permutations if and only if the underlying graph is complete. We then introduce a generalized graph-based construction using a non-commutative two-qudit gate, denoted $GR$, which requires directed edges and an explicit vertex ordering. We show that complete directed graphs generate fully antisymmetric multipartite states when endowed with appropriate orientations. Together, these results provide a unified graph-theoretic description of bosonic and fermionic exchange symmetry based on graph completeness and edge orientation. |
| title | Symmetric and Antisymmetric Quantum States from Graph Structure and Orientation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.19857 |