Monitoring and compensating method for mode dispersion based on density matrix theory

The invention relates to a mode dispersion monitoring compensation method and system based on a density matrix theory. The method comprises the following steps: constructing a mode dispersion compensation matrix based on the density matrix theory by utilizing a definition formula of a group delay matrix in the density matrix theory and unitary property of a transmission matrix for describing field state evolution in an optical fiber; meanwhile, construction of a specific form of a matrix is completed according to the Hermite property of the group delay matrix and the spatial dimension of the mode, then key elements capable of fully describing mode dispersion state information in the matrix are extracted, and real-time tracking and iterative updating are carried out on the key elements, so that monitoring compensation of mode dispersion in the system is achieved. The method does not need any auxiliary matrix, can be directly applied to tracking of spatial mode dispersion of any dimension mode, and completes re