Pauli矩阵的性质与应用

Basic Properties and Applications of Pauli Matrix

通过Pauli矩阵基本数值指标及基本性质、矩阵函数、矩阵谱分解及矩阵张量积,研究Pauli矩阵的相关性质及在量子信息中的部分应用.深化了Pauli矩阵的性质,刻画了r·σ矩阵的性质,给出Hermite矩阵及密度矩阵的Bloch向量表示、获得Pauli矩阵函数和密度矩阵函数的有关结果.为纯态矩阵的判断、密度矩阵的距离度量等量子信息论研究提供了丰富的资源.

In this paper,the properties of Pauli matrix and its applications in quantum information are studied through the basic numerical index and properties of Pauli matrix,matrix function,matrix spectral decomposition and matrix tensor product.The properties of Pauli matrix are deepened,the properties of matrix r·σare characterized,the Bloch vector representation of Hermite matrix and density matrix are given,and the relevant results of Pauli matrix function and density matrix function are obtained.It provides abundant resources for studies on quantum information theory such as the judgment of pure state matrix and the distance measurement of density matrix,etc.