Entanglement of a class of non-Gaussian states in disordered harmonic oscillator systems

TL;DR

This paper develops a new method to exactly calculate the bipartite entanglement, specifically logarithmic negativity, of non-Gaussian states in disordered harmonic oscillator systems on a lattice, revealing an area law for low energy states.

Contribution

A novel approach for exact entanglement calculation in non-Gaussian states of disordered harmonic oscillators, with proven bounds and area law behavior.

Findings

Exact logarithmic negativity for the states was derived.

Entanglement bounds were established.

Low energy states follow an area law.

Abstract

For disordered harmonic oscillator systems over the $d$-dimensional lattice, we consider the problem of finding the bipartite entanglement of the uniform ensemble of the energy eigenstates associated with a particular number of modes. Such ensemble define a class of mixed, non-Gaussian entangled states that are labeled, by the energy of the system, in an increasing order. We develop a novel approach to find the exact logarithmic negativity of this class of states. We also prove entanglement bounds and demonstrate that the low energy states follow an area law.