A Symplectic Proof of the Quantum Singleton Bound

Frederick Dehmel; Shilun Li

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arXiv · 2602.20186

A Symplectic Proof of the Quantum Singleton Bound

Frederick Dehmel·Shilun Li

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Abstract

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.

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Frederick Dehmel, Shilun Li. 2026-02-21. A Symplectic Proof of the Quantum Singleton Bound. https://arxiv.org/abs/2602.20186

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