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

TL;DR

This paper presents an all-versus-nothing proof of genuine tripartite EPR steering, establishing a method to certify tripartite entanglement in a two-sided device-independent scenario through logical contradiction and a generalized steering inequality.

Contribution

It introduces a novel all-versus-nothing proof for tripartite EPR steering and formulates a new 2SDI steering inequality for certifying genuine tripartite entanglement.

Findings

Logical contradiction distinguishes GGHZ and W-class states.

Maximum violation of the tripartite FGI certifies genuine entanglement.

Proof applies to three-qubit pure states in a 2SDI scenario.

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.