论文标题
使用Majorana Star表示，测量学和无效相位曲线的几何分解
Geometric decomposition of geodesics and null phase curves using Majorana star representation
论文作者
论文摘要
地球学是给定表面上任意两个点之间的最短曲线。量子系统状态空间中的大地学在几何阶段理论中起重要作用，因为这些也是所获得的几何相为零的曲线。无效相曲线（NPC）是地球学的概括，该曲线被定义为沿着所获得的几何相沿曲线为零的曲线，即使它们不必是两个点之间的最短曲线。在这里，我们提出了高维状态空间中的几何分解和NPC的几何分解，从而可以理解这些曲线的内在对称性。我们使用Majoraana Star代表来分解$ n $二维的Hilbert Space在Bloch Sphere上的$ N-1 $曲线，并表明所有$ N-1 $曲线都是圆形细分市场，其特定属性由特定的特定属性由给定的GeoDesic依次连接的最终状态的内部产品确定。我们还提出了一种使用我们的几何分解，以$（n> 2）$ - 尺寸希尔伯特空间以$（n> 2）$（n> 2）$（n> 2）$（n> 2）$（n> 2）构建无限的NPC。
Geodesics are the shortest curves between any two points on a given surface. Geodesics in the state space of quantum systems play an important role in the theory of geometric phases, as these are also the curves along which the acquired geometric phase is zero. Null phase curves (NPCs) are the generalization of the geodesics, which are defined as the curves along which the acquired geometric phase is zero even though they need not be the shortest curves between two points. Here we present a geometric decomposition of geodesics and NPCs in higher-dimensional state space, which allows understanding the intrinsic symmetries of these curves. We use Majorana star representation to decompose a geodesic in the $n$-dimensional Hilbert space to $n-1$ curves on the Bloch sphere and show that all the $n-1$ curves are circular segments with specific properties that are determined by the inner product of the end states connected by the given geodesic. We also propose a method to construct infinitely many NPCs between any two arbitrary states for $(n>2)$-dimensional Hilbert space using our geometric decomposition.
