Local Statistical Properties of Schmidt Eigenvalues of Bipartite Entanglement for a Random Pure State

Consider the model of bipartite entanglement for a random pure state emerging in quantum information and quantum chaos, corresponding to the fixed trace Laguerre unitary ensemble (LUE) in random matrix theory. We focus on correlation functions of Schmidt eigenvalues for the model and prove universal limits of the correlation functions in the bulk and also at the soft and hard edges of the spectrum, as that of LUE. Further, we consider the bounded trace LUE and obtain the same universal limits.