论文标题
截短的力矩序列和通道可分离性问题的解决方案
Truncated moment sequences and a solution to the channel separability problem
论文作者
论文摘要
我们考虑通过Choi-Jamiołkowski同构给出的Choi矩阵表示量子通道的可分离性问题。我们探索了系统和Ancillae之间不同切割的三类可分离性，并根据Choi状态的坐标（以固定的基础）为截断的力矩序列（TMS）$ y $的绘制提供了一个解决方案。这导致了一种算法，该算法使用半决赛编程提供可分离性证书。计算复杂性及其性能取决于TMS中变量$ n $的数量，以及订单$ t $的矩阵$ m_t（y）$的矩量的大小。我们利用算法来研究2 Quit和单Qutrit通道家族的分离性；在后一种情况下，我们可以根据否定性$ n $的标准提供一个示例的答案，该标准对于$ n = 0 $的choi矩阵仍然没有定论。
We consider the problem of separability of quantum channels via the Choi matrix representation given by the Choi-Jamiołkowski isomorphism. We explore three classes of separability across different cuts between systems and ancillae and we provide a solution based on the mapping of the coordinates of the Choi state (in a fixed basis) to a truncated moment sequence (tms) $y$. This results in an algorithm which gives a separability certificate using semidefinite programming. The computational complexity and the performance of it depend on the number of variables $n$ in the tms and on the size of the moment matrix $M_t(y)$ of order $t$. We exploit the algorithm to numerically investigate separability of families of 2-qubit and single-qutrit channels; in the latter case we can provide an answer for examples explored earlier through the criterion based on the negativity $N$, a criterion which remains inconclusive for Choi matrices with $N=0$.
