在 LU 等价下对 2 和 3 量子比特态密度矩阵的分类
量子物理
2025-04-25 v4
摘要
在本文中，我们给出了 Jing-Yang-Zhao 论文《量子态的局域幺正等价与同时正交等价》中证明的修改版本，该证明建立了 量子比特的局域幺正等价与同时正交等价之间的对应关系。我们的修改证明利用了超矩阵代数框架，通过该框架，我们能够将这种对应关系推广到 量子比特。最后，我们应用 Specht 准则的推广（首次在 V. Futorney、R. A. Horn 和 V. V. Sergeichuk 的《线性映射系统的 Specht 准则》中证明），将 量子比特的局域幺正等价问题简化为检查迹恒等式及其他几个易于检查的性质。我们还指出，如果我们将 LU 等价的概念放宽为 Jing 等人在上述论文中定义的准 LU 等价，所有这些结果都可以推广到 和 量子特。
引用
@article{arxiv.2404.07338,
title = {Classifying Density Matrices of 2 and 3 Qubit States Up To LU Equivalence},
author = {Isaac Dobes and Naihuan Jing},
journal= {arXiv preprint arXiv:2404.07338},
year = {2025}
}
备注
There were mistakes in this paper. They have been corrected and uploaded in a separate submission to arXiv under arXiv:2503.06240. I kindly request that this paper be taken down since the submission corresponding to the aforementioned ID is superior to this paper and does not contain any errors, and so at this point there is no reason for this paper to remain up