Four-Qubit Monogamy and Four-Way Entanglement

TL;DR

This paper investigates four-qubit monogamy relations and their ability to define four-way entanglement measures, finding that simple weighted inequalities cannot serve as SLOCC-invariant entanglement measures.

Contribution

It analyzes the properties of four-qubit monogamy relations and demonstrates the limitations of using weighted inequalities for four-way entanglement measures.

Findings

Minimal power factors for monogamy relations identified

Weighted inequalities do not yield SLOCC-invariant four-way entanglement measures

Analysis extends understanding of multi-qubit entanglement constraints

Abstract

We examine the various properties of the three four-qubit monogamy relations, all of which introduce the power factors in the three-way entanglement to reduce the tripartite contributions. On the analytic ground as much as possible we try to find the minimal power factors, which make the monogamy relations hold if the power factors are larger than the minimal powers. Motivated to the three-qubit monogamy inequality we also examine whether those four-qubit monogamy relations provide the SLOCC-invariant four-way entanglement measures or not. Our analysis indicate that this is impossible provided that the monogamy inequalities are derived merely by introducing weighting power factors.