Experimental demonstration of the Bell-type inequalities for four qubit Dicke state using IBM Quantum Processing Units

TL;DR

This paper demonstrates the violation of Bell-type inequalities for two- and four-qubit Dicke states on IBM Quantum Processors, highlighting the impact of state preparation methods and error mitigation on observing quantum nonlocality.

Contribution

It introduces a tailored Bell-type inequality for Dicke states and compares gate-based and statevector-based preparation methods on real quantum hardware.

Findings

Bell inequality violations observed on IBM QPUs for two and four qubits.

Error mitigation techniques improve violation measurements.

Statevector-based method shows more robustness against noise.

Abstract

Violation of the Bell-type inequalities is necessary to confirm the existence of nonlocality in nonclassical (entangled) states. We have designed a customized operator which is made of the sum of the Pauli matrices ($\sigma_x$, $\sigma_y$, and $\sigma_z$). We theoretically and experimentally investigate the violation of Bell-type inequalities using two- and four-qubit Dicke states on IBM Quantum Processing Units (QPUs). We compare two different state preparation methods for the four-qubit Dicke state -- gate-based and statevector-based -- and evaluate their performance on two IBM QPUs, \texttt{ibm\_kyiv} and \texttt{ibm\_sherbrook}. For the two-qubit case, we demonstrate clear violations of the CHSH inequality, with the highest observed Bell parameter reaching $2.821 \pm 0.0019$ using M3 error mitigation, which is within $0.7\sigma$ of the theoretical maximum $2\sqrt{2}$. In the four-qubit case, we employ a Bell-type inequality tailored for Dicke states and achieve a maximum violation of $2.607 \pm 0.029$ without the need for additional mitigation when using the statevector-based method. Our results reveal that advanced error mitigation techniques significantly enhance the observed violations in the gate-based method, while the statevector-based approach inherently yields more robust states with lower noise. This study highlights the critical role of state preparation and mitigation techniques in probing fundamental quantum correlations on near-term quantum hardware.