Multipartite Monogamy of Entanglement for Three Qubit States

TL;DR

This paper investigates the distribution of quantum entanglement in three-qubit states, establishing monogamy relations using genuine multipartite and bipartite entanglement measures, with analytical and numerical results for GHZ and W states.

Contribution

It introduces a novel monogamy relation involving source entanglement and bipartite entanglement measures for three-qubit states, with analytical proofs and numerical support.

Findings

Square of source entanglement bounds bipartite entanglement sums in GHZ states

Analytical demonstration for GHZ class states with exceptions

Numerical evidence supports monogamy relation for W class states

Abstract

The distribution of entanglement in a multiparty system can be described through the principles of monogamy or polygamy. Monogamy is a fundamental characteristic of entanglement that restricts its distribution among several number of parties(more than two). In this work, our aim is to explore how quantum entanglement can be distributed in accordance with monogamy relations by utilizing both the genuine multipartite entanglement measures and bipartite entanglement measures. Specifically, we treat source entanglement as the genuine multipartite entanglement measure and use the entanglement of formation specifically for bipartite cases. For GHZ class states, we analytically demonstrate that the square of the source entanglement serves as an upper bound for the sum of the squares of the entanglement of formation of the reduced subsystems, with some exceptions for specific non-generic GHZ states. We also present numerical evidence supporting this result for W class states. Additionally, we explore the monogamy relation by using accessible entanglement as an upper bound.