Entanglement negativity spectrum of random mixed states: A diagrammatic approach

Understand

The entanglement properties of random pure states are relevant to a variety of problems ranging from chaotic quantum dynamics to black hole physics.

• The averaged bipartite entanglement entropy of such states admits a volume law and upon increasing the subregion size follows the Page curve.
• In this paper, we generalize this setup to random mixed states by coupling the system to a bath and use the partial transpose to study their entanglement properties.
• We develop a diagrammatic method to incorporate partial transpose within random matrix theory and formulate a perturbation theory in $1/L$, the inverse of the Hilbert space dimension.