In the present work we study tripartite quantum steering of quantum correlations arising from two local dichotomic measurements on each side in the two types of partially device-independent scenarios: the one-sided device-independent scenario where one of the parties performs untrusted measurements while the other two parties perform trusted measurements and the two-sided device-independent scenario where one of the parties performs trusted measurements while the other two parties perform untrusted measurements. We demonstrate that tripartite steering in the two-sided device-independent scenario is weaker than tripartite steering in the one-sided device-independent scenario by using two families of quantum correlations. That is, these two families of quantum correlations in the two-sided device-independent framework detect tripartite entanglement through tripartite steering for a larger region than that in the one-sided device-independent framework. It is shown that tripartite steering in the two-sided device-independent scenario implies the presence of genuine tripartite entanglement of $2\times 2\times 2$ quantum system, even if the correlation does not exhibit genuine nonlocality or genuine steering.

• Received 2 November 2017

DOI:https://doi.org/10.1103/PhysRevA.98.022101