Local statistical properties of Schmidt eigenvalues of bipartite entanglement for a random pure state

TL;DR

This paper investigates the local statistical properties of Schmidt eigenvalues in bipartite entanglement for random pure states, demonstrating universal behavior in correlation functions across different spectral regions.

Contribution

It establishes universal limits of correlation functions for Schmidt eigenvalues in the fixed trace and bounded trace Laguerre unitary ensembles, extending results to quantum entanglement models.

Findings

Universal correlation function limits in the bulk spectrum

Universal limits at soft and hard spectral edges

Extension of results to bounded trace LUE

Abstract

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 these for the LUE. Further we consider the bounded trace LUE and obtain the same universal limits.