用黎曼几何刻画退极化量子信道
Characterizing the Depolarizing Quantum Channel in Terms of Riemannian Geometry
摘要：
我们探讨了黎曼几何工具的概念上的有用性，诱导的统计概念，在量化的效果去极化信道上的量子态的可扩展性。具体来说，我们比较了二维希尔伯特空间上与密度算子相关的未变形和变形布洛赫球内部的几何形状。我们发现，随机化出现几何通过一个较小的无穷小量子线元素变形布洛赫球，而均匀收缩体现自己通过变形的测地线的空间分量变形的四布洛赫矢量的简单的压缩版本的未变形布洛赫矢量分量。
英文摘要：
We explore the conceptual usefulness of Riemannian geometric tools induced by the statistical concept of distinguishability in quantifying the effect of a depolarizing channel on quantum states. Specifically, we compare the geometries of the interior of undeformed and deformed Bloch spheres related to density operators on a two-dimensional Hilbert space. We show that randomization emerges geometrically through a smaller infinitesimal quantum line element on the deformed Bloch sphere while the uniform contraction manifests itself via a deformed set of geodesics where the spacial components of the deformed four-Bloch vector are simply the contracted versions of the undeformed Bloch vector components.
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