论文标题
寻找有效的纠缠证人操作员，以获取双方量子系统中的约束纠缠状态
Search for an efficient entanglement witness operator for bound entangled states in bipartite quantum systems
论文作者
论文摘要
纠缠检测问题是量子信息理论中的重要问题之一。古尔维特（Gurvit）表明，这个问题是NP完成的，因此这可能是仅一个标准不足以检测所有纠缠状态的可能原因。有一些强大的纠缠检测标准，例如部分换位标准，重组标准，但在实验中可能无法成功实施它们。如果通过构建证人操作员方法检测到纠缠，则可以避免这种情况。在这项工作中，我们采用一种分析方法来构建证人操作员。为了实现此任务，我们首先使用部分换位和重组操作构建线性图。然后，我们在地图的参数上找到一些条件，该参数代表地图代表正面地图。此外，我们已经构建了与地图相对应的CHOI矩阵，并表明它不是完全正面的。然后，我们构建了一个纠缠证人操作员，该操作员基于Choi矩阵和身份矩阵的函数的线性组合，并且可以检测NPTES和PPTES。最后，我们通过检测几个以前未被某些众所周知的可分离性标准所发现的两部分结合的状态来证明其效率。我们还将证人操作员的检测能力与三个众所周知的强大纠缠检测标准，即DV标准，CCNR标准和基于Sarbicki Et提出的相关性张量（CT）的可分离性标准。 al。并发现我们的证人操作员发现的纠缠状态比这些标准更纠缠。
Entanglement detection problem is one of the important problem in quantum information theory. Gurvit showed that this problem is NP complete and thus this may be the possible reason that only one criterion is not sufficient to detect all entangled states. There are some powerful entanglement detection criterion such as partial transposition criterion, realignment criterion but it may not be possible to implement them successfully in the experiment. This situation can be avoided if the entanglement is detected through the construction of witness operator method. In this work, we take an analytical approach to construct a witness operator. To achieve this task, we first construct a linear map using partial transposition and realignment operation. Then we find some conditions on the parameters of the map for which the map represent a positive map. Further, we have constructed a Choi matrix corresponding to the map and have shown that it is not completely positive. We then construct an entanglement witness operator, which is based on the linear combination of the function of Choi matrix and the identity matrix and it can detect both NPTES and PPTES. Finally, we prove its efficiency by detecting several bipartite bound entangled states which were previously undetected by some well-known separability criteria. We also compared the detection power of our witness operator with three well-known powerful entanglement detection criteria, namely, dV criterion, CCNR criterion and the separability criteria based on correlation tensor (CT) proposed by Sarbicki et. al. and find that our witness operator detect more entangled states than these criterion.
