Experimental Detection of Non-local Correlations using Navascues-Pironio-AcınHierarchy in the Tripartite States*

It has been shown, by Navascues et al, that fewer body correlations can reveal the non-local
nature of the correlations arising from the quantum mechanical description of nature. Such tests
on the correlations can be transformed into a semi-definite-program (SDP). Here we present the experimental implementation of Navascues-Pironio-Acın (NPA) hierarchy on NMR hardware utilizing
three nuclear spins. The protocol has been tested on two types of genuine tripartite entangled states.
In both the cases, experimentally measured correlations were used to formulate the SDP under
linear constraints on the entries of the moment matrix. It has been observed that in both the cases
SDP failed to find a semi-definite-positive moment matrix consistent with the experimental data
which indeed the signature that the observed correlations can not arise from local measurements on
a separable state and hence non-local in nature. This also confirms that both the states under test
are indeed entangled. Results have been verified by direct full quantum state tomography in each
case.