Tetrahedron genuine entanglement measure of four-qubit systems

TL;DR

This paper introduces a novel geometric measure called the concurrence tetrahedron to quantify genuine four-qubit entanglement, providing a more comprehensive and discriminative tool than previous measures.

Contribution

The paper constructs a new genuine four-qubit entanglement measure based on the volume of a concurrence tetrahedron, extending the quantification framework for multipartite entanglement.

Findings

The measure can classify bi-separable entanglement in non-genuine states.

It is not equivalent to existing genuine four-partite entanglement concurrence.

The measure demonstrates advantages through detailed examples.

Abstract

Quantifying genuine entanglement is a key task in quantum information theory. We study the quantification of genuine multipartite entanglement for four-qubit systems. Based on the concurrence of nine different classes of four-qubit states, with each class being closed under stochastic local operation and classical communication, we construct a concurrence tetrahedron. Proper genuine four-qubit entanglement measure is presented by using the volume of the concurrence tetrahedron. For non genuine entangled pure states, the four-qubit entanglement measure classifies the bi-separable entanglement. We show that the concurrence tetrahedron based measure of genuine four-qubit entanglement is not equivalent to the genuine four-partite entanglement concurrence. We illustrate the advantages of the concurrence tetrahedron by detailed examples.