Multi-linear Monogamy Relations for Three Qubit States

TL;DR

This paper generalizes monogamy relations of entanglement for multi-qubit systems using entanglement of formation and concurrence, providing criteria for genuine entanglement and analyzing maximally entangled states, with applications to three-qubit states.

Contribution

It introduces a multi-linear monogamy relation for multi-qubit states and explores its implications for entanglement criteria and maximally entangled states.

Findings

Derived a generalized monogamy relation for multi-qubit systems.

Proposed an entanglement criterion for genuine entangled states.

Analyzed absolutely maximally entangled states for three qubits.

Abstract

The monogamy of entanglement means that entanglement cannot be freely shared. In 2014, Oliveira et al. [ Oliveira et al., Phys. Rev. A. 89, 034303 (2014)] proposed a monogamy relation in the linear version and considered it in terms of entanglement of formation. Here we generalize the above version and consider a multi-linear monogamy relation for a multi-qubit system in terms of entanglement of formation and concurrence. Based on the above results, we present an entanglement criterion for genuine entangled states, also we consider the absolutely maximally entangled states and present what an absolutely maximally entangled state is for a three-qubit system. At last, we apply our results to a three-qubit pure state in terms of quantum discord.