A Symplectic Proof of the Quantum Singleton Bound
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915896123981824 |
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| author | Dehmel, Frederick Li, Shilun |
| author_facet | Dehmel, Frederick Li, Shilun |
| contents | We present a symplectic linear-algebraic proof of the Quantum Singleton Bound for stabiliser quantum error-correcting codes together with a Lean4 formalisation of the linear-algebraic argument. The proof is formulated in the language of finite-dimensional symplectic vector spaces modelling Pauli operators and relies on distance-based erasure correctability and the cleaning lemma. Using a dimension-counting argument within the symplectic stabiliser framework, we derive the bound $k + 2(d-1) \le n$ for any $[[n, k, d]]$ stabiliser code. This approach isolates the algebraic structure underlying the bound and avoids the heavier analytic machinery that appears in entropy-based proofs, while remaining well-suited to formal verification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Symplectic Proof of the Quantum Singleton Bound Dehmel, Frederick Li, Shilun Quantum Physics Information Theory 81P70, 94B05, 15A63 We present a symplectic linear-algebraic proof of the Quantum Singleton Bound for stabiliser quantum error-correcting codes together with a Lean4 formalisation of the linear-algebraic argument. The proof is formulated in the language of finite-dimensional symplectic vector spaces modelling Pauli operators and relies on distance-based erasure correctability and the cleaning lemma. Using a dimension-counting argument within the symplectic stabiliser framework, we derive the bound $k + 2(d-1) \le n$ for any $[[n, k, d]]$ stabiliser code. This approach isolates the algebraic structure underlying the bound and avoids the heavier analytic machinery that appears in entropy-based proofs, while remaining well-suited to formal verification. |
| title | A Symplectic Proof of the Quantum Singleton Bound |
| topic | Quantum Physics Information Theory 81P70, 94B05, 15A63 |
| url | https://arxiv.org/abs/2602.20186 |