Limits for entanglement distribution with separable states

Entanglement distribution with separable states has recently attracted considerable attention. Recent results suggest that quantum discord, a measure for quantum correlations beyond entanglement, is responsible for this counterintuitive phenomenon. In this work we study this question from a different perspective and find minimal requirements for a separable state to be useful for entanglement distribution. Surprisingly, we find that the presence of quantum discord is not sufficient to ensure entanglement distribution: There exist states with nonzero quantum discord that nevertheless cannot be used for entanglement distribution. As a result, we show that entanglement distribution is not possible with rank-2 separable states. Our work sheds light on the task of entanglement distribution with separable states and reveals a classification of quantum states with respect to their usefulness for this task.

Figure 1

A quantum system consisting of two parties $A$ and $B$ (upper figure) is useful for entanglement distribution if party $B$ can be divided in two parties $B_1$ and $B_2$ (middle figure) in such a way that sending particle $A$ from side 1 to side 2 leads to an increase of entanglement (lower figure).

Figure 2

Entanglement distribution with separable states by sending a qutrit: The plot shows the amount of distributed entanglement $\Delta E_n=E_n^{B_1|B_{2}A}-E_n^{A{B}_1|B_2}$ for the state given in Eq. (4) as a function of the parameter $\alpha$. For details see the main text.

Figure 3

Entanglement distribution with separable states by sending a single qubit: The plot shows the amount of distributed entanglement $\Delta E_n=E_n^{B_1|B_{2}A}-E_n^{A{B}_1|B_2}$ for the state given in Eq. (5) as a function of the parameter $\alpha$. For details see the main text.