Extreme Eigenvalues of Wishart Matrices: Application to Entangled Bipartite System

Understand

We discuss an application of the random matrix theory in the context of estimating the bipartite entanglement of a quantum system.

• We discuss how the Wishart ensemble (the earliest studied random matrix ensemble) appears in this quantum problem.
• The eigenvalues of the reduced density matrix of one of the subsystems have similar statistical properties as those of the Wishart matrices, except that their {\em trace is constrained to be unity}.
• We focus here on the smallest eigenvalue which serves as an important measure of entanglement between the two subsystems.