核逆和核偏序的刻画

Characterizations of the Core Inverse and the Core Partial Ordering

研究矩阵核逆的相关性质和基于核逆的核偏序的等价刻画。通过对Pauli矩阵的矩阵类型、数值刻画、代数关系等的研究,得出Pauli矩阵的性质。利用Pauli矩阵的性质,推得Pauli矩阵在量子信息中的应用,如密度矩阵的Bloch表示、Pauli矩阵的函数、Tsirelson不等式和密度矩阵的常用度量表示。

A study is made of the related properties of the matrix core inverse and the equivalent characterization of the core partial order based on the core inverse. The properties of the Pauli matrix are obtained through the research of the Pauli matrix’s type, numerical characterization, algebraic relations and so on. Using the properties of Pauli matrix, the application of Pauli matrix in quantum information is deduced, such as the Bloch representation of density matrix, the function of Pauli matrix,Tsirelson’s inequality and the common metric representation of density matrix.