On the Cleaning Lemma of Quantum Coding Theory
Quantum Physics
2022-05-17 v1 Information Theory
math.IT
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.
Cite
@article{arxiv.2204.04699,
title = {On the Cleaning Lemma of Quantum Coding Theory},
author = {Gleb Kalachev and Sergey Sadov},
journal= {arXiv preprint arXiv:2204.04699},
year = {2022}
}
Comments
25pp