Experimental demonstration of the Bell-type inequalities for four qubit
  Dicke state using IBM Quantum Processing Unit
Violation of the Bell-type inequalities is very necessary to confirm the
existence of the nonlocality in the nonclassical (entangled) states. We have
designed a customized operator which is made of the sum of the identity and
Pauli matrices ($I$, $\sigma_x$, $\sigma_y$, and $\sigma_z$). We theoretically
evaluate the Bell-type violation for the two-qubit Bell state and a four-qubit
Dicke state, which gives the Bell-CHSH parameter values $2\sqrt{2}$ and $3.05$,
respectively for our customized operator. For experimental implementation,
IBM's 127-qubitQuantum Processing Units (QPU) were utilized, where we have
applied our customized operator to evaluate Bell-type inequalities for
two-qubit Bell state ($\vert\Phi^+\rangle$) and four-qubit Dicke state
($|D^{(2)}_4\rangle$). We observed, for the two-qubit Bell state, the
experimental Bell violation was $2.7507\pm 0.0197$. For Dicke state, we found
the violation be to $2.1239\pm0.0457$ and $2.2175\pm0.0352$ respectively for
two distinct methods of state preparation. All our results show clear violation
of the local realism; however, we find that the experimental violation of the
Bell state ($2.75$) is close to the theoretical ($2.82$) results due to lower
circuit depth in state-preparation as well as fewer measurements, while the
Dicke state shows greater errors ($2.12$ and $2.21$ vs. $3.05$) from higher
depth and more measurements.
 Tomis Harsh Mehta Shreya Banerjee Prasanta K. Panigrahi V. Narayanan