Equivalence of Quantum Single Insertion and Single Deletion Error-Correctabilities, and Construction of Codes and Decoders

This article contributes to an unsolved quantum information problem: the equivalence between insertion error-correctability and deletion error-correctability. The solution in Shibayama and Ouyang’s sense is provided in the single-error under the assumption of the purity of quantum codeword states On the other hand, a class of codes that can correct both single deletion and single insertion is provided.