Symmetry protected entanglement in random mixed states

TL;DR

This paper investigates how Abelian symmetries affect entanglement in random mixed quantum states, deriving explicit formulas and phase diagrams, and proposing a quantum circuit simulation method.

Contribution

It introduces a diagrammatic and perturbative approach to analyze symmetry-protected entanglement negativity in random states with Abelian symmetries, providing new analytical tools and phase diagrams.

Findings

Explicit formulas for negativity in symmetric sectors

Identification of qualitative differences due to symmetry

Design of a quantum circuit for simulation

Abstract

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. We further present entanglement phase diagrams as the subsystem sizes are varied and show that there are qualitative differences between systems with and without symmetries. We also design a quantum circuit to simulate our setup.