Genuine Einstein-Podolsky-Rosen steering of three-qubit states by multiple sequential observers

Abstract

We investigate the possibility of multiple uses of a single copy of a three-qubit state for detecting genuine tripartite Einstein-Podolsky-Rosen (EPR) steering. A pure three-qubit state of either the Greenberger-Horne-Zeilinger (GHZ) type or $W$ type is shared between two fixed observers in two wings and a sequence of multiple observers in the third wing who perform unsharp or nonprojective measurements. The measurement settings of each of the multiple observers in the third wing are independent and uncorrelated with the measurement settings and outcomes of the previous observers. In such setup, we investigate all possible types of ($2\ensuremath{\rightarrow}1$) and ($1\ensuremath{\rightarrow}2$) genuine tripartite EPR steering. For each case, we obtain an upper limit on the number of observers on the third wing who can demonstrate genuine EPR steering through the quantum violation of an appropriate tripartite steering inequality. We show that the GHZ state allows for a higher number of observers compared to the $W$ state. Additionally, ($1\ensuremath{\rightarrow}2$) genuine steering is possible for a larger range of sharpness parameters compared to ($2\ensuremath{\rightarrow}1$) genuine steering cases.