二子系密度矩阵谱分解的取迹方法

The Matrix Trace Method For Spectral Resolution of Bipartite Systems

利用su(N)代数的生成元给出了二子系密度矩阵的最一般表达式,进而导出了密度矩阵的任意次整幂的递推公式。在此基础上,提出了密度矩阵谱分解的取迹方法,给出了相关的计算公式。最后,展望了取迹方法在量子信息及量子力学的定域不变量理论中的可能应用。

By using the generators of su （N） algebra the most general expression for the density matrix of bipartite systems has been given. Furthermore, the successive iteration formulas for calculating any power of density matrix are derived. Then, we proposed the matrix trace method for spectral resolution of density matrix and all the correlative formulas are given. At the end, we forecast still possible applications in the theory of local invariants in quantum mechanics and quantum information.