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On the Cleaning Lemma of Quantum Coding Theory
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On the Cleaning Lemma of Quantum Coding Theory
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The term "Cleaning Lemma" refers to a family of similar propositions that have been used in Quantum Coding Theory to estimate the minimum distance of a code in terms of its length and dimension. We show that the mathematical core is a simple fact of linear algebra of inner product spaces; moreover, it admits a further reduction to a combinatorial, lattice-theoretical level. Several concrete variants of the Cleaning Lemma and some additional propositions are derived as corollaries of the proposed approach.
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Cited by 1 Pith paper
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A Symplectic Proof of the Quantum Singleton Bound
The quantum Singleton bound k+2(d−1)≤n for stabilizer codes is derived from erasure correctability and the cleaning lemma, and formalized in Lean4.
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