Local unitary equivalence of orthogonal arrays and related linear codes
Abstract
Orthogonal arrays (OAs) are combinatorial configurations with applications in experimental design, error-correcting codes, and quantum information. Local unitary (LU) equivalence provides a natural framework for classifying multipartite entangled states. Using the correspondence between OAs and quantum states, Goyeneche and Życzkowski [Phys. Rev. A, 2014, 90: 022316] posed the problem of determining when OAs are LU equivalent. In this paper, we construct OAs from generator matrices and establish conditions for Fourier-based LU equivalence of OAs and irredundant orthogonal arrays (IrOAs). For prime alphabets, we identify the Fourier partners of the linear OAs considered here with the arrays of their corresponding dual codes. This gives an explicit connection between LU equivalence and coding theory. We also identify families of LU equivalent OAs arising from specific classes of linear codes.
Related
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BibTeX
@misc{zheng2026local,
title = {{Local unitary equivalence of orthogonal arrays and related linear codes}},
author = {Miaomiao Zheng and Yajuan Zang and Xiuling Shan and Zihong Tian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19811},
eprint = {2609.19811},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19811},
}
RIS
TY - UNPB
TI - Local unitary equivalence of orthogonal arrays and related linear codes
AU - Miaomiao Zheng
AU - Yajuan Zang
AU - Xiuling Shan
AU - Zihong Tian
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19811
UR - https://arxiv.org/abs/2609.19811
AB - Orthogonal arrays (OAs) are combinatorial configurations with applications in experimental design, error-correcting codes, and quantum information. Local unitary (LU) equivalence provides a natural framework for classifying multipartite entangled states. Using the correspondence between OAs and quantum states, Goyeneche and Życzkowski [Phys. Rev. A, 2014, 90: 022316] posed the problem of determining when OAs are LU equivalent. In this paper, we construct OAs from generator matrices and establish conditions for Fourier-based LU equivalence of OAs and irredundant orthogonal arrays (IrOAs). For prime alphabets, we identify the Fourier partners of the linear OAs considered here with the arrays of their corresponding dual codes. This gives an explicit connection between LU equivalence and coding theory. We also identify families of LU equivalent OAs arising from specific classes of linear codes.
ER -