四量子比特纠缠的九种方式及其三角化
The nine ways of four qubit entanglement and their threetangle
摘要：
我计算了在Phys.Rev.A { \bf 65}，052112（2002）中发现的四量子比特代表态的约化密度矩阵的混合三角$τ_3[ρ]$。在大多数情况下，凸屋顶，除了一类，我提供了一个新的上限，这是假设非常接近凸屋顶。我比较结果发表在物理评论快报。{ \bf 113}，110501（2014）。由于在那里应用的方法通常会导致较高的上限值，在某些情况下，可以理解，凸屋顶是准确获得的，即当$τ_3$消失的零多面体收缩到一个单一的点。
英文摘要：
I calculate the mixed threetangle $τ_3[ρ]$ for the reduced density matrices of the four-qubit representant states found in Phys. Rev. A {\bf 65}, 052112 (2002). In most of the cases, the convex roof is obtained, except for one class, where I provide with a new upper bound, which is assumed to be very close to the convex roof. I compare with results published in Phys. Rev. Lett. {\bf 113}, 110501 (2014). Since the method applied there usually results in higher values for the upper bound, in certain cases it can be understood that the convex roof is obtained exactly, namely when the zero-polytope where $τ_3$ vanishes shrinks to a single point.
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