论文标题
纠缠量化的线性半无限编程方法
Linear semi-infinite programming approach for entanglement quantification
论文作者
论文摘要
我们通过将其识别为线性半官方编程（LSIP）问题来探讨凸屋顶构造的双重问题。使用LSIP理论，我们表明了原始问题和双重问题之间没有二元性差距，即使纠缠量词不是连续的，并且证明了最佳解决方案的集合是非空的且有限的。此外，我们为LSIP实施了一种中央的先知平面算法，以量化三个量子位之间的纠缠。该算法具有全球收敛性，并为非最佳可行点的纠缠措施提供了较低的界限。作为应用程序，我们使用该算法来计算三角形的凸屋顶和$π$ tangle的措施，该量度低和高级的国家家庭。由于$π$ - 键入度量量化了w状态的纠缠，因此我们应用两个量化器的值来区分两种不同类型的真正的三分之三纠缠。
We explore the dual problem of the convex roof construction by identifying it as a linear semi-infinite programming (LSIP) problem. Using the LSIP theory, we show the absence of a duality gap between primal and dual problems, even if the entanglement quantifier is not continuous, and prove that the set of optimal solutions is non-empty and bounded. In addition, we implement a central cutting-plane algorithm for LSIP to quantify entanglement between three qubits. The algorithm has global convergence property and gives lower bounds on the entanglement measure for non-optimal feasible points. As an application, we use the algorithm for calculating the convex roof of the three-tangle and $π$-tangle measures for families of states with low and high ranks. As the $π$-tangle measure quantifies the entanglement of W states, we apply the values of the two quantifiers to distinguish between the two different types of genuine three-qubit entanglement.
