Multipartite monogamy of the concurrence

TL;DR

This paper introduces a new monogamous relation in quantum entanglement involving multipartite concurrence, extending the understanding of entanglement sharing in three-qubit systems and highlighting limitations for larger systems.

Contribution

It presents a novel monogamous equality involving multipartite and bipartite concurrences for three-qubit pure states, and extends to inequalities for mixed states, with a counter-example for larger systems.

Findings

New monogamous equality for three-qubit pure states

Extension to mixed states via inequalities

Counter-example showing limits for systems with more than three qubits

Abstract

Monogamy of entanglement is generally discussed using a bipartite entanglement measure as an upper bound. Here we discuss a new kind of monogamous relation where the upper bound is given by a multipartite measure of entanglement, the generalized concurrence. We show a new monogamous equality involving the multipartite concurrence, all the bipartite concurrences and the genuine tripartite entanglement for pure three qubits system. The result extends to mixed states in an inequality involving the generalized concurrence and all the bipartite concurrences. We provide a counter-example showing that the result cannot be extended for systems with more than three qubits.