New MDS Entanglement-Assisted Quantum Codes from MDS Hermitian Self-Orthogonal Codes
Hao Chen

TL;DR
This paper introduces a method to construct new MDS entanglement-assisted quantum codes from Hermitian self-orthogonal codes, expanding the possibilities for quantum error correction with nonzero entanglement consumption.
Contribution
It establishes an equivalence between Hermitian self-orthogonal codes and Hermitian hull codes, enabling the transformation of known codes into entanglement-assisted quantum codes.
Findings
Existence of MDS EAQEC codes with nonzero c for lengths up to q^2+1.
Transformation of Hermitian self-orthogonal codes into multiple EAQEC codes.
Extension of quantum MDS code constructions to entanglement-assisted scenarios.
Abstract
The intersection of a linear code and its Hermitian dual is called the Hermitian hull of this code. A linear code satisfying is called Hermitian self-orthogonal. Many Hermitian self-orthogonal codes were given for the construction of MDS quantum error correction codes (QECCs). In this paper we prove that for a nonnegative integer satisfying , a linear Hermitian self-orthogonal code is equivalent to a linear -dimension Hermitian hull code. Therefore a lot of new MDS entanglement-assisted quantum error correction (EAQEC) codes can be constructed from previous known Hermitian self-orthogonal codes. Actually our method shows that previous constructed quantum MDS codes from Hermitian self-orthogonal…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Coding theory and cryptography
