Entanglement in random pure states: Spectral density and average von Neumann entropy

TL;DR

This paper derives exact spectral densities and average von Neumann entropy for entanglement in random pure states across different invariant classes, revealing maximum entanglement in the symplectic class.

Contribution

It provides closed-form expressions for spectral densities and average entropy for all three invariant classes of random matrix ensembles, advancing understanding of entanglement properties.

Findings

Maximum average entanglement in the symplectic class

Exact spectral density expressions for all classes

Analytical results for average von Neumann entropy

Abstract

Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt eigenvalues. We derive here closed expressions for the spectral density of Schmidt eigenvalues for all three invariant classes of random matrix ensembles. We also obtain exact results for average von Neumann entropy. We find that maximum average entanglement is achieved if the system belongs to the symplectic invariant class.