This work studies the Clifford algebra approach to the density matrix. We discuss elementary examples of pure and mixed states by writing the density matrix as an element of the Clifford algebra of the three-dimensional space \(Cl_3\). We also revisit the phenomenon of Larmor precession within the framework of Clifford algebra. Additionally, we discuss the geometrical interpretation of the so-called Clifford Density Element (CDE) for pure states in analogy to the Bloch sphere of conventional quantum theory. Finally, we discuss the dynamics of the CDE, which obeys an algebraic form of the Liouville von–Neumann equation.

中文翻译：

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密度矩阵的克利福德代数：一种基本方法

这项工作研究密度矩阵的克利福德代数方法。我们通过将密度矩阵写为三维空间 \(Cl_3\) 的 Clifford 代数的元素来讨论纯态和混合态的基本例子。我们还在克利福德代数的框架内重新审视拉莫尔进动现象。此外，我们还讨论了纯态的所谓克利福德密度元 (CDE) 的几何解释，类似于传统量子理论的布洛赫球。最后，我们讨论 CDE 的动力学，它遵循刘维尔·冯·诺依曼方程的代数形式。