论文标题
绝对纠缠的纯状态
Absolutely entangled set of pure states
论文作者
论文摘要
最近，Cai等人。 [ARXIV：2006.07165V1]提出了一个新概念“绝对纠缠的量子”系统：对于任何可能的全球基础选择，该集合的至少一个状态是纠缠的。他们在那里提出了一个最低限度的示例，其中有两个量子系统中的四个州，并提出了对绝对集纠缠的定量措施。在这项工作中，我们得出了两个必需条件，使一组状态成为绝对纠缠的集合。此外，我们在$ \ mathbb {c}^{d_1} \ otimes \ mathbb {c}^{d_2} $上提供了绝对纠缠的基础的串联构造。此外，基于$ \ mathbb {c}^2 \ otimes \ mathbb {c}^n $中的正交产品基础的结构，我们获得了$ 2N+1 $元素的另一个绝对纠缠套装的结构，$ \ mathbb {c}^2 \ otimes \ otimes \ otimes \ otimes \ otimimes \ otmathbbbbbb {c}^n $。
Quite recently, Cai et al. [arXiv:2006.07165v1] proposed a new concept "absolutely entangled set" for bipartite quantum systems: for any possible choice of global basis, at least one state of the set is entangled. There they presented a minimum example with a set of four states in two qubit systems and they proposed a quantitative measure for the absolute set entanglement. In this work, we derive two necessity conditions for a set of states to be an absolutely entangled set. In addition, we give a series constructions of absolutely entangled bases on $\mathbb{C}^{d_1}\otimes \mathbb{C}^{d_2}$ for any nonprime dimension $d=d_1\times d_2$. Moreover, based on the structure of the orthogonal product basis in $\mathbb{C}^2\otimes \mathbb{C}^n$, we obtain another construction of absolutely entangled set with $2n+1$ elements in $\mathbb{C}^2\otimes \mathbb{C}^n$.
