AI 中文总结
本研究将适用于三量子比特纯态的并发三角形及并发填充扩展至混合态，提出并发棱柱几何框架，解析得到GHZ与W态非相干混合的并发填充闭式表达式，为多体纠缠量化提供可视化方法。
AI 中文摘要
多体纠缠的量化仍是量子信息理论中一个长期存在的开放性挑战，对量子基础和量子技术具有重要意义。在三量子比特纯态的语境下，并发三角形是多种多体纠缠度量的几何解释基础；其中，与并发三角形面积平方根成正比的并发填充（concurrence fill）已被证实是一种有效的真正三体纠缠度量。因此，当前学界对将并发三角形和并发填充扩展至三量子比特混合态存在浓厚兴趣。本研究表明，任意秩-2三量子比特混合态均可通过与其纯态分解关联的并发棱柱进行可视化；由此，通过凸屋顶扩展得到的混合态并发填充，与所有纯态分解下取最小值的、定义为底面积乘以高度平方根的总棱柱填充面积成正比。随后，我们考虑格林伯格-霍恩-蔡林格（GHZ）态与W态的非相干混合构成的三量子比特混合态，解析地执行其凸屋顶扩展，得到这类秩-2混合态并发填充的闭式表达式。最后，我们将并发棱柱的几何图像应用于这些混合态及其对应最小并发填充的纯态分解，作为可视化工具使用。
英文摘要
The quantification of multipartite entanglement remains a long-standing open challenge in quantum information theory with major implications for quantum foundations and quantum technologies. In the context of three-qubit pure states, the concurrence triangle underlies geometric interpretations for a variety of multipartite entanglement measures. In particular, the concurrence fill, which is proportional to the square root of the area of the concurrence triangle, has been shown to be a valid measure of genuine tripartite entanglement. As a result, there is now significant interest in extending the concurrence triangle and concurrence fill to three-qubit mixed states. In this work, we show that any rank-2 three-qubit mixed state can be visualized in terms of concurrence prisms associated with their pure state decompositions. Thus, the concurrence fill of the mixed state obtained through convex-roof extension is proportional to the total prism fill area, defined as the square root of the base area times the height, associated with the prisms minimized over all pure state decompositions. We then consider three-qubit mixed states that are incoherent mixtures of Greenberger-Horne-Zeilinger (GHZ) and W states and analytically perform their convex-roof extension to obtain a closed-form expression for the concurrence fill of these rank-2 mixtures. Finally, we apply the geometric picture of concurrence prisms to these mixtures and their pure state decomposition corresponding to minimum concurrence fill as a tool for visualization.
Comments9 pages, 4 figures
