Entanglement of three-qubit random pure states

TL;DR

This paper investigates the non-local properties and entanglement classifications of three-qubit pure states generated randomly, providing distributions, invariants, and entanglement measures to deepen understanding of their quantum correlations.

Contribution

It introduces new probability distributions, classifies states into four entanglement classes, and characterizes these classes using polynomial invariants and entanglement polytopes.

Findings

Distributions of coefficients and phases for random states

Classification of states into four entanglement classes

Characterization of classes via polynomial invariants and entanglement polytopes

Abstract

We study non-local properties of generic three-qubit pure states. First, we obtain the distributions of both the coefficients and the only phase in the five-term decomposition of Ac\'in et al. for an ensemble of random pure states generated by the Haar measure on U(8). Furthermore, we analyze the probability distributions of two sets of polynomial invariants. One of these sets allows us to classify three-qubit pure states into four classes. Entanglement in each class is characterized using the minimal R\'enyi-Ingarden-Urbanik entropy. Besides, the fidelity of a three-qubit random state with the closest state in each entanglement class is investigated. We also present a characterization of these classes and the SLOCC classes in terms of the corresponding entanglement polytope.