We explore the possibility of multiple usage of a single genuine entangled state by considering a scenario consisting of three spin-$\frac{1}{2}$ particles shared between Alice, Bob, and multiple Charlies. Alice performs measurements on the first particle, Bob performs measurements on the second particle, and multiple Charlies perform measurements on the third particle sequentially. Here the choice of measurement settings of each Charlie is independent and uncorrelated with the choices of measurement settings and outcomes of the previous Charlies. In this scenario, we investigate whether more than one Charlie can detect genuine tripartite entanglement, and we answer this question affirmatively. In order to probe genuine entanglement, we use correlation inequalities the violations of which certify genuine tripartite entanglement in a device-independent way. We extend our investigation by using appropriate genuine tripartite entanglement witness operators. Using each of these different tools for detecting genuine tripartite entanglement, we find out the maximum number of Charlies who can detect genuine entanglement in the above scenario.

• Received 25 October 2019
• Accepted 2 April 2020

DOI:https://doi.org/10.1103/PhysRevA.101.042340