AI 中文总结
提出一种由两个布洛赫球和纠缠分量构成的双量子比特纯态可视化方法，证明其参数化为全局微分同胚，并用于展示条件态、纠缠自由度和单比特旋转。
AI 中文摘要
我提出一种用于纯双量子比特态的简单可视化方法，它由三个部分组成：两个布洛赫球分别表示边缘量子比特（即分别忽略另一个量子比特后得到的混合态），以及一个由旋转反射和收缩构成的纠缠分量。我证明了该图像能准确捕捉相关态空间的局部与全局结构，且无间隙或简并：其底层参数化是到态空间上的全局微分同胚。最后，我用该图像可视化条件态、纠缠自由度以及单量子比特旋转。
英文摘要
I propose a simple visualization for pure two-qubit states, constructed from three components: two Bloch balls for the marginal qubits (the mixed states obtained by ignoring the other qubit, respectively) and an entanglement component consisting of a rotoreflection and a contraction. I prove that this picture accurately captures the local and global structure of the relevant state space without gaps or degeneracies: the underlying parametrization is a global diffeomorphism onto the state space. Finally, I use this picture to visualize conditional states, the entanglement degree(s) of freedom, and single qubit rotations.
