Chruściński Dariusz, Bera Anindita, Bae Joonwoo, Hiesmayr Beatrix C
Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudzia̧dzka 5/7, 87-100, Toruń, Poland.
Department of Mathematics, Birla Institute of Technology Mesra, 835215, Jharkhand, India.
Sci Rep. 2025 Aug 2;15(1):28205. doi: 10.1038/s41598-025-10985-0.
Two approaches can be utilized to handle the separability problem, finding out whether a given bipartite qudit state is separable or not: a direct procedure on the state space or the effective tool of entanglement witnesses (EWs). This contribution studies the structure of EWs. Exploiting the very concept of mirrored EWs, increasing the detection power, we show, in contrast to the conjecture in a recent paper (Bera et al. in Sci Rep 13:10733, 2023), there exist pairs of optimal EWs, which are both non-decomposible, i.e. can detect bound/PPT-entangled states in an optimal way. Since we show that the structure also extends to higher dimensions, our results reveal a further structure of entanglement witnesses.
可以采用两种方法来处理可分离性问题，即确定给定的二分量子态是否可分离：一种是在态空间上的直接程序，另一种是纠缠见证者（EWs）的有效工具。本文研究了纠缠见证者的结构。利用镜像纠缠见证者的概念，提高检测能力，我们发现，与最近一篇论文（Bera等人，《科学报告》，2023年，第13卷，第10733页）中的猜想相反，存在一对最优纠缠见证者，它们都是不可分解的，即能够以最优方式检测束缚/PPT纠缠态。由于我们表明这种结构也扩展到更高维度，我们的结果揭示了纠缠见证者的进一步结构。
