Monogamy of the Entanglement of Formation

Understand

We show that any measure of entanglement that on pure bipartite states is given by a strictly concave function of the reduced density matrix is monogamous on pure tripartite states.

• This includes the important class of bipartite measures of entanglement that reduce to the (von Neumann) entropy of entanglement.
• Moreover, we show that the convex roof extension of such measures (e.g., entanglement of formation) are monogamous also on \emph{mixed} tripartite states.
• To prove our results, we use the definition of monogamy without inequalities, recently put forward[Gour and Guo, Quantum \textbf{2}, 81 (2018)].