Voronoi图与量子信道容量的数值估计
Voronoi Diagrams and a Numerical Estimation of a Quantum Channel Capacity
摘要：
给出了量子纯态的一种新的几何解释。利用Voronoi图，我们将纯态空间的结构重新解释为量子态空间的一个子空间。除了已知的单量子比特纯态的一些Voronoi图的重合之外，我们还将证明，即使对于混合的单量子比特态，只要位置被给定为纯态，Voronoi图相对于某些距离-发散度，Bures距离和Euclidean距离-都是相同的。对于更高能级的纯量子态，对于发散度、Fubini-Study距离和Bures距离，图的重合性仍然成立，而关于发散度和欧氏距离的图的重合性不再成立。当我们试图将用于数值估计单量子比特量子信道容量的方法应用于更高级别的系统时，这一事实具有重要意义。
英文摘要：
We give a new geometric interpretation of quantum pure states. Using Voronoi diagrams, we reinterpret the structure of the space of pure states as a subspace of the quantum state space. In addition to the known coincidence of some Voronoi diagrams for one-qubit pure states, we will show that even for mixed one-qubit states, as far as sites are given as pure states, the Voronoi diagram with respect to some distances -- the divergence, the Bures distance, and the Euclidean distance -- are all the same. As to higher level pure quantum states, for the divergence, the Fubini-Study distance, and the Bures distance, the coincidence of the diagrams still holds, while the coincidence of the diagrams with respect to the divergence and the Euclidean distance no longer holds. That fact has a significant meaning when we try to apply the method used for a numerical estimation of a one-qubit quantum channel capacity to a higher level system.
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