Monogamy of the Entanglement of Formation

TL;DR

This paper proves that a broad class of entanglement measures, including entanglement of formation, are monogamous on both pure and mixed tripartite quantum states, emphasizing monogamy as an intrinsic property of quantum entanglement.

Contribution

It establishes the monogamy property for measures defined by strictly concave functions and their convex roof extensions, generalizing previous results.

Findings

Entanglement measures based on strictly concave functions are monogamous on pure tripartite states.

Convex roof extensions of such measures are monogamous on mixed tripartite states.

Monogamy of entanglement is an inherent property of quantum entanglement itself.

Abstract

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)]. Our results promote the theme that monogamy of entanglement is a property of quantum entanglement and not an attribute of some particular measures of entanglement.