Quantum Deletion Codes derived from Classical Deletion Codes (Extended Abstract)

TL;DR

This paper introduces a new method for constructing quantum deletion error-correcting codes from classical deletion codes, achieving higher code rates close to 1, which surpasses previous quantum code rates.

Contribution

It proposes a code construction condition that enables deriving quantum deletion codes from classical ones, with examples correcting single-quantum deletions and high code rates.

Findings

Quantum codes correcting single-quantum deletion errors

Code rates arbitrarily close to 1

New construction method from classical deletion codes

Abstract

This manuscript is an extended abstract version of the paper entitled ``Quantum Deletion Codes derived from Classical Deletion Codes.'' The paper contributes to the fundamental theory for quantum deletion error-correcting codes. The paper proposes a code construction condition for a partition of classical deletion error-correcting codes to derive quantum deletion error-correcting codes. The construction methods in this paper give examples of quantum codes that can correct single-quantum deletion errors and have a code rate arbitrarily close to 1, while the previously known quantum deletion code rates are close to 0 for long length. This manuscript omits the proofs of the statements in the paper.