量子比特系统上正映射锥的拓扑
Topology of the cone of positive maps on qubit systems
摘要：
给出了矩阵代数$M_{2}(\mathbb{C})$的正映射分解的一个已知定理的另一种几何证明。证明的前提是在四维空间中确定具有保持Lorentz锥的算子的正映射，并且它允许将正映射相对于保持锥边界的正映射进行分解。此外，还给出了$M_{2}(\mathbb{C})$的映射完全正的一些有用条件，以及$M_{n}(\mathbb{C})$的极值Schwarz映射完全正的一个充分条件.最后，按照同样的几何方法，在拓扑方面的描述，同时是完全积极的和完全共正的地图已提交。
英文摘要：
An alternative, geometrical proof of a known theorem concerning the decomposition of positive maps of the matrix algebra $M_{2}(\mathbb{C})$ has been presented. The premise of the proof is the identification of positive maps with operators preserving the Lorentz cone in four dimensions, and it allows to decompose the positive maps with respect to those preserving the boundary of the cone. In addition, useful conditions implying complete positivity of a map of $M_{2}(\mathbb{C})$ have been given, together with a sufficient condition for complete positivity of an extremal Schwarz map of $M_{n}(\mathbb{C})$. Lastly, following the same geometrical approach, a description in topological terms of maps that are simultaneously completely positive and completely copositive has been presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
