Stabiliser codes over fields of even order
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909308203040768 |
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| author | Ball, Simeon Moreno, Edgar Simoens, Robin |
| author_facet | Ball, Simeon Moreno, Edgar Simoens, Robin |
| contents | We prove that the natural isomorphism between GF(2^h) and GF(2)^h induces a bijection between stabiliser codes on n quqits with local dimension q=2^h and binary stabiliser codes on hn qubits. This allows us to describe these codes geometrically: a stabiliser code over a field of even order corresponds to a so-called quantum set of symplectic polar spaces. Moreover, equivalent stabiliser codes have a similar geometry, which can be used to prove the uniqueness of a [[4,0,3]]_4 stabiliser code and the nonexistence of both a [[7,1,4]]_4 and an [[8,0,5]]_4 stabiliser code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabiliser codes over fields of even order Ball, Simeon Moreno, Edgar Simoens, Robin Combinatorics Information Theory Quantum Physics 94B27 We prove that the natural isomorphism between GF(2^h) and GF(2)^h induces a bijection between stabiliser codes on n quqits with local dimension q=2^h and binary stabiliser codes on hn qubits. This allows us to describe these codes geometrically: a stabiliser code over a field of even order corresponds to a so-called quantum set of symplectic polar spaces. Moreover, equivalent stabiliser codes have a similar geometry, which can be used to prove the uniqueness of a [[4,0,3]]_4 stabiliser code and the nonexistence of both a [[7,1,4]]_4 and an [[8,0,5]]_4 stabiliser code. |
| title | Stabiliser codes over fields of even order |
| topic | Combinatorics Information Theory Quantum Physics 94B27 |
| url | https://arxiv.org/abs/2401.06618 |