张量算符的对称适应分解与耦合自旋系统的可视化
Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
摘要：
我们研究有限维量子系统的表示和可视化。在广义维格纳表示中，多自旋算子可以被分解成一个自适应的张量基，它们被映射到多个球面图上，每个球面图都是由球谐函数的线性组合组成的。我们采用两种不同的方法，基于显式投影算子和分数的父母的系数，以获得这个基础上多达六个自旋1/2（量子比特），其中各种例子。提供了对具有任意自旋数（qudits）的两个耦合自旋的扩展，还突出了自旋1/2耦合到自旋1（qutrit）的量子系统。
英文摘要：
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple spherical plots that are each assembled from linear combinations of spherical harmonics. We apply two different approaches based on explicit projection operators and coefficients of fractional parentage in order to obtain this basis for up to six spins 1/2 (qubits), for which various examples are presented. An extension to two coupled spins with arbitrary spin numbers (qudits) is provided, also highlighting a quantum system of a spin 1/2 coupled to a spin 1 (qutrit).
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