论文标题
高维状态空间的形状：Qutrit的Bloch-Ball类似物
The shape of higher-dimensional state space: Bloch-ball analog for a qutrit
论文作者
论文摘要
几何直觉是一种至关重要的工具，可以更深入地了解许多物理概念。其功率的一个范式示例是Bloch Ball，这是最简单的量子系统的状态空间的几何表示，即两级系统（或Qubit）。但是，对于三级系统（QUTRIT），状态空间已经具有八个维度，因此其复杂性超过了我们三维经验空间的掌握。不幸的是，鉴于描述QUTRIT的状态空间的几何对象具有更丰富的结构，并且在许多方面，对于一般量子系统而言，其代表性比量子系统更具代表性。在这项工作中，我们证明，基于量子状态的Bloch表示，可以为Qutrit状态空间构建一个三维模型，该模型捕获后者的大多数基本几何特征。除了具有无可争辩的理论价值外，这还为新的表示形式打开了大门，从而将我们的几何直觉扩展到了最简单的量子系统之外。
Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system, a two-level system (or qubit). However, already for a three-level system (qutrit) the state space has eight dimensions, so that its complexity exceeds the grasp of our three-dimensional space of experience. This is unfortunate, given that the geometric object describing the state space of a qutrit has a much richer structure and is in many ways more representative for a general quantum system than a qubit. In this work we demonstrate that, based on the Bloch representation of quantum states, it is possible to construct a three dimensional model for the qutrit state space that captures most of the essential geometric features of the latter. Besides being of indisputable theoretical value, this opens the door to a new type of representation, thus extending our geometric intuition beyond the simplest quantum systems.
