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arXiv · 2410.20241

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

Tomis Prajapati·Harsh Mehta·Shreya Banerjee·Prasanta K. Panigrahi·V. Narayanan
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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.

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Tomis Prajapati, Harsh Mehta, Shreya Banerjee, Prasanta K. Panigrahi, V. Narayanan. 2024-10-26. Experimental demonstration of the Bell-type inequalities for four qubit Dicke state using IBM Quantum Processing Units. https://doi.org/10.1002/qute.202500366

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