Experimental construction of a symmetric three-qubit entangled state and its utility in testing the violation of a Bell inequality on an NMR quantum simulator

TL;DR

This paper reports the experimental creation of a symmetric three-qubit entangled state on an NMR quantum processor and demonstrates its utility in testing Bell inequality violations.

Contribution

The authors designed and experimentally realized a permutation-symmetric maximally entangled three-qubit state and used it to test a specific Bell inequality.

Findings

Successfully prepared the $ ext{S}$ state on NMR platform

Certified entanglement via negativity and concurrence

Observed maximal violation of Bell inequality 26

Abstract

We designed a quantum circuit to prepare a permutation-symmetric maximally entangled three-qubit state called the $\vert {\rm S} \rangle$ state and experimentally created it on an NMR quantum processor. The presence of entanglement in the state was certified by computing two different entanglement measures, namely negativity and concurrence. We used the $\vert {\rm S} \rangle$ state in conjunction with a set of maximally incompatible local measurements, to demonstrate the maximal violation of inequality number $26$ in Sliwa's classification scheme, which is a tight Bell inequality for the (3,2,2) scenario i.e. the three party, two measurement settings and two measurement outcomes scenario.