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arXiv · 2204.04699

On the Cleaning Lemma of Quantum Coding Theory

Gleb Kalachev·Sergey Sadov
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Abstract

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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Gleb Kalachev, Sergey Sadov. 2022-04-10. On the Cleaning Lemma of Quantum Coding Theory. https://doi.org/10.1016/j.laa.2022.05.002

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