Gupta, Shashank; Das, Debarshi; Jebarathinam, Chellasamy; Roy, Arup; Datta, Shounak; Majumdar, AS; (2022) “All-versus-nothing” proof of genuine tripartite steering and entanglement certification in the two-sided device-independent scenario. Quantum Studies: Mathematics and Foundations , 9 pp. 175-198. 10.1007/s40509-021-00261-x.

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Abstract

We consider the task of certification of genuine entanglement of tripartite states. For this purpose, we first present an "all-versus-nothing" proof of genuine tripartite Einstein-Podolsky-Rosen (EPR) steering by demonstrating the non-existence of a hybrid local hidden state (LHS) model in the tripartite network as a motivation to our main result. A full logical contradiction of the predictions of the hybrid LHS model with quantum mechanical outcome statistics for any three-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) states and pure W-class states is shown. Using logical contradiction, we can distinguish between the GGHZ and W-class state in a two-sided device-independent (2SDI) steering scenario. We next formulate a 2SDI steering inequality which is a generalization of the fine-grained steering inequality (FGI) derived in \cite{PKM14} for the tripartite scenario. We show that the maximum quantum violation of this tripartite FGI can be used to certify genuine entanglement of three-qubit pure states.

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