A large-N approximated field theory for multipartite entanglement

TL;DR

This paper introduces a large-N approximation method for analyzing multipartite entanglement in quantum systems, revealing a phase transition and the disappearance of entanglement frustration in the limit of large N.

Contribution

It generalizes the characterization of multipartite entanglement by replacing complex numbers with real vectors, enabling large-N analysis and uncovering new phenomena.

Findings

Identification of a phase transition in multipartite entanglement

Demonstration that entanglement frustration vanishes at large N

Development of a large-N approximation framework for entanglement analysis

Abstract

We study the characterization of multipartite entanglement for the random states of an $n$-qbit system. Unable to solve the problem exactly we generalize it, changing complex numbers into real vectors with $N_c$ components (the original problem is recovered for $N_c=2$). Studying the leading diagrams in the large-$N_c$ approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the large-$N_c$ limit.