近日，杭州电子科技大学的张林及其研究小组取得一项新进展。经过不懈努力，他们通过部分转置矩成功可视化了所有双量子比特态。相关研究成果已于2023年7月11日在国际知名学术期刊《物理评论A》上发表。

该研究小组通过涉及第四个部分转置矩（PT矩）(两个量子比特态的最后一个PT矩)来可视化所有两个量子比特态对应的三维(3D)区域。通过优化一些多项式，最终实现了对这个双量子比特态所对应的三维区域的表征。此外，研究人员确定了整个三维区域的两个部分之间的分界面，分别对应于纠缠态和可分离态。由于部分转置矩的可测量性，研究人员得到了一个完整的、可操作的双量子比特纠缠判据。

据悉，有效检测基于可测量的纠缠是量子信息处理的一个基本问题。最近，人们提出了可测量的部分转置矩作为一种方法来解决这个问题。在最近的研究中，研究人员成功确定了对应于双量子比特纠缠态的二维区域，该区域由第二和第三部分转置矩构成，并描述了所有双量子比特态的整个区域。

附：英文原文

Title: Visualization of all two-qubit states via partial-transpose moments

Author: Lin Zhang, Yi Shen, Hua Xiang, Quan Qian, Bo Li

Issue&Volume: 2023/07/11

Abstract: Efficiently detecting entanglement based on measurable quantities is a basic problem for quantum information processing. Recently, the measurable quantities called partial-transpose (PT) moments have been proposed to detect and characterize entanglement. Recently [L. Zhang et al., Ann. Phys. (Berlin) 534, 2200289 (2022)], we have already identified the two-dimensional region, comprised of the second and third PT moments, corresponding to two-qubit entangled states, and described the whole region for all two-qubit states. In the present paper, we visualize the three-dimensional (3D) region corresponding to all two-qubit states by further involving the fourth PT moment (the last one for two-qubit states). The characterization of this 3D region can finally be achieved by optimizing some polynomials. Furthermore, we identify the dividing surface which separates the two parts of the whole 3D region corresponding to entangled and separable states, respectively. Due to the measurability of PT moments, we obtain a complete and operational criterion for the detection of two-qubit entanglement.

DOI: 10.1103/PhysRevA.108.012414

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.108.012414