多体系统中完全对称态的可分性
量子物理
2019-03-27 v4
摘要
对称性在量子力学领域中起着重要作用。在本文中，我们考虑多体系统 中对称量子态的一个子类，即完全对称态，它在任意指标置换下不变。L. Qian 和 D. Chu [arXiv:1810.03125 [quant-ph]] 猜想完全对称态可分当且仅当它是对称纯乘积态的凸组合。在本文中，我们证明了该猜想在二体和多体情形下均成立。并且我们证明了完全对称态 在其秩不超过 或 时可分。对于秩为 或 的态，它们可分当且仅当其值域包含一个乘积向量。我们将结果应用于量子信息中一些广泛有用的态，如对称态、边缘态、极值态和非负态。我们还研究了 CS 态与 Hankel 矩阵和 Toeplitz 矩阵的关系。
引用
@article{arxiv.1812.04182,
title = {Separability of Completely Symmetric States in Multipartite System},
author = {Lin Chen and Delin Chu and Lilong Qian and Yi Shen},
journal= {arXiv preprint arXiv:1812.04182},
year = {2019}
}
备注
The abstract, introduction and conclusion have been revised. The bibliography was also changed. Some language mistakes have been corrected. Some phrased have been changed to make it more concise and clearer. And the order of the authors' name (First and Second names) have been exchanged. The addresses of the authors has also been verified. arXiv admin note: text overlap with arXiv:1810.03125 by other authors