Measurement-device-independent entanglement and randomness estimation in quantum networks

Detection of entanglement in quantum networks consisting of many parties is one of the important steps toward building quantum communication and computation networks. We consider a scenario where the measurement devices used for this certification are uncharacterized. In this case, it is well known that by using quantum states as inputs for the measurement devices it is possible to detect any entangled state (a situation known as measurement-device-independent entanglement witnessing). Here we go beyond entanglement detection and provide methods to estimate the amount of entanglement in a quantum network. We also consider the task of randomness certification and show that randomness can be certified in a variety of cases, including single-partite experiments or setups using only separable states.

Figure 1

Min-entropy ($-log{G}_{x^{*}{y}^{*}}$) vs noise $w$ for the probability distribution that arises by performing Bell state measurements on the two-qubit Werner state, and quantum inputs along the vertices of a tetrahedron on the Bloch sphere. For all $w\ne 0$ (i.e., whenever the state is not equal to the maximally mixed state), then randomness can be certified. This graph was produced using the cvx [57] package for matlab and the toolbox qetlab [58].