Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits

TL;DR

This paper investigates whether the monogamy relations of entanglement, well-established for three qubits, can be extended to systems with more than three qubits, finding that such generalizations are unlikely.

Contribution

The study explores potential extensions of monogamy relations to four-qubit systems and demonstrates the limitations of such generalizations.

Findings

Generalized monogamy relations are unlikely to exist beyond three qubits.

Polynomial invariants characterize entanglement in four-qubit states.

Examples show that existing monogamy equality cannot be straightforwardly extended.

Abstract

We discuss the possibility to interpret the residual entanglement for more than three qubits in terms of distributed multipartite entanglement, or, in other words, possible extensions of the Coffman-Kundu-Wootters monogamy equality to higher qubit numbers. Existing knowledge on entanglement in multipartite systems puts narrow constraints on the form of such extensions. We study various examples for families of pure four-qubit states for which the characterization of three-qubit and four-qubit entanglement in terms of polynomial invariants is known. These examples indicate that, although families with such extensions do exist, a generalized monogamy equality cannot be found along those lines.