Insertion Correcting Capability for Quantum Deletion-Correcting Codes

TL;DR

This paper establishes a link between quantum deletion-correcting codes and insertion errors, introduces a quantum indel distance, and characterizes the correction capabilities of quantum codes.

Contribution

It proves that quantum t-deletion-correcting codes can also correct certain insertion errors and defines a quantum indel distance for analyzing error correction.

Findings

Quantum t-deletion-correcting codes also correct certain insertion errors.

Introduces the quantum indel distance for error analysis.

Characterizes the correction capability of quantum codes using this distance.

Abstract

This paper proves that any quantum t-deletion-correcting codes also correct a total of t insertion and deletion errors under a certain condition. Here, this condition is that a set of quantum states is defined as a quantum error-correcting code if the error spheres of its states are disjoint, as classical coding theory. In addition, this paper proposes the quantum indel distance and describes insertion and deletion errors correcting capability of quantum codes by this distance.