Symmetry protected entanglement in random mixed states

Understand

Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium.

• In this paper, we study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space.
• In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with $\mathbb{Z}_N$ and $U(1)$ symmetry groups.
• To this end, we develop a diagrammatic method to incorporate partial transpose within the random matrix theory of symmetric states and formulate a perturbation theory in the inverse of the Hilbert space dimension.