A linear-algebraic and lattice-theoretical look at the Cleaning Lemma of quantum coding theoryстатьяИсследовательская статья
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Дата последнего поиска статьи во внешних источниках: 13 июля 2022 г.
Аннотация: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.