Device-Independent Entanglement Quantification and Related Applications

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on the observed data only but independent of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device-independent entanglement witnesses involving an arbitrary number of parties.

Figure 1

Negativity bounds for violations close to the maximum of the Bell inequality $I_{3322}$ [37, 38] obtained by solving Eq. (4) for different levels of the moment matrix. Note that violations with $v>0.25$ require a negativity of $N[{\rho }_{AB}]>1/2$ and thus at least a two-qutrit state.