Monogamy Relations for Multiqubit Systems

TL;DR

This paper critically analyzes monogamy relations in multiqubit systems using squared negativity, confirming their validity in three qubits but revealing violations in certain four-qubit states through analytical and numerical evidence.

Contribution

It extends the understanding of monogamy relations by testing their validity with squared negativity in four-qubit states, showing limitations of previous relations.

Findings

Monogamy relations hold for three-qubit pure states with squared negativity.

Violations of monogamy relations occur in some four-qubit pure states.

Analytical and numerical evidence supports the existence of these violations.

Abstract

Recently a new class of monogamy relations (actually, exponentially many) was provided by Christopher Eltschka et al. in terms of squared concurrence. Their approach restricted to the distribution of bipartite entanglement shared between different subsystems of a global state. We have critically analyzed those monogamy relations in three as well as in four qubit pure states using squared negativity. We have been able to prove that in case of pure three qubit states those relations are always true in terms of squared negativity. However, if we consider the pure four qubit states, the results are not always true. Rather, we find opposite behaviour in some particular classes of four qubit pure states where some of the monogamy relations are violated. We have provided analytical and numerical evidences in support of our claim.