The injective norm of CSS quantum error-correcting codes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914117611159552 |
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| author | Dartois, Stephane Zémor, Gilles |
| author_facet | Dartois, Stephane Zémor, Gilles |
| contents | In this paper, we compute the injective norm - a.k.a. geometric entanglement - of standard basis states of CSS quantum error-correcting codes. The injective norm of a quantum state is a measure of genuine multipartite entanglement. Computing this measure is generically NP-hard. However, it has been computed exactly in condensed-matter theory - notably in the context of topological phases - for the Kitaev code and its extensions, in works by Orús and collaborators. We extend these results to all CSS codes and thereby obtain the injective norm for a nontrivial, infinite family of quantum states. In doing so, we uncover an interesting connection to matroid theory and Edmonds' intersection theorem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_23736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The injective norm of CSS quantum error-correcting codes Dartois, Stephane Zémor, Gilles Quantum Physics Mathematical Physics Combinatorics 81P42, 81P45, 81P73, 05B35 In this paper, we compute the injective norm - a.k.a. geometric entanglement - of standard basis states of CSS quantum error-correcting codes. The injective norm of a quantum state is a measure of genuine multipartite entanglement. Computing this measure is generically NP-hard. However, it has been computed exactly in condensed-matter theory - notably in the context of topological phases - for the Kitaev code and its extensions, in works by Orús and collaborators. We extend these results to all CSS codes and thereby obtain the injective norm for a nontrivial, infinite family of quantum states. In doing so, we uncover an interesting connection to matroid theory and Edmonds' intersection theorem. |
| title | The injective norm of CSS quantum error-correcting codes |
| topic | Quantum Physics Mathematical Physics Combinatorics 81P42, 81P45, 81P73, 05B35 |
| url | https://arxiv.org/abs/2510.23736 |