"All-versus-nothing" proof of tripartite quantum steering and genuine entanglement certification in the two-sided device-independent scenario

Shashank Gupta, Debarshi Das, Chellasamy Jebarathinam, Arup Roy, Shounak Datta, A. S. Majumdar

Published Oct 28, 2019• 0 citations

Abstract

We consider the task of certification of genuine entanglement of tripartite states. We first present an all-versus-nothing proof of tripartite Einstein-Podolsky-Rosen (EPR) steering by demonstrating the non-existence of a 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 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 which, one can distinguish between the GGHZ and W-class states in the two-sided device-independent (2SDI) steering scenario. We next formulate a 2SDI fine-grained steering inequality for the tripartite scenario. We show that the maximum quantum violation of this FGI can be used to certify genuine entanglement of three-qubit pure states.

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