On the Cleaning Lemma of Quantum Coding Theory

DOI10.1016/J.LAA.2022.05.002arXiv2204.04699WikidataQ114151559 ScholiaQ114151559MaRDI QIDQ6396136

Publication date: 10 April 2022

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.

Mathematics Subject Classification ID

Vector spaces, linear dependence, rank, lineability (15A03) Modular lattices, complemented lattices (06C99) Computational stability and error-correcting codes for quantum computation and communication processing (81P73)

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