New monogamy relations for multiqubit systems

Recently, a new class of monogamy relations (actually, exponentially many) was provided by Christopher Eltschka et al. in terms of squared concurrence. Their approach is restricted to the distribution of bipartite entanglement shared between different subsystems of a global state. We have critically analysed those monogamy relations in three as well as in four-qubit pure states using squared negativity. We have been able to prove that in the 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.

Automated summary

In this study, new monogamy relations based on concurrence were proposed, and their validity in three-qubit and four-qubit pure states were analyzed using squared negativity. The findings suggest that while the relations hold true in pure three-qubit states, they are not always valid in pure four-qubit states, with some specific classes exhibiting violations of monogamy relations. Analyses and numerical evidence were provided to support these conclusions.