Strong monogamy inequalities for four qubits

TL;DR

This paper explores the limitations of extending the Coffman-Kundu-Wootters monogamy inequality to four qubits, analyzing violations and proposing alternative constraints through numerical studies.

Contribution

It identifies the failure of the natural extension of the monogamy inequality and investigates new possible inequalities for four-qubit entanglement sharing.

Findings

The natural extension of the monogamy inequality does not hold universally.

Violations of the inequality are characterized in detail.

Numerical analysis explores properties of alternative inequalities.

Abstract

We investigate possible generalizations of the Coffman-Kundu-Wootters monogamy inequality to four qubits, accounting for multipartite entanglement in addition to the bipartite terms. We show that the most natural extension of the inequality does not hold in general, and we describe the violations of this inequality in detail. We investigate alternative ways to extend the monogamy inequality to express a constraint on entanglement sharing valid for all four-qubit states, and perform an extensive numerical analysis of randomly generated four-qubit states to explore the properties of such extensions.