Experimental Verification of Bell‐Type Inequalities Using Four‐Qubit Dicke States on Quantum Processors

Abstract

Testing for a violation of Bell‐type inequalities provides a standard approach to investigating nonlocal correlations in nonclassical (entangled) states. In this study, a custom measurement operator composed of a linear combination of Pauli matrices ( σx$\sigma _x$ , σy$\sigma _y$ , and σz$\sigma _z$ ) is constructed to examine such violations. Both theoretical and experimental analyses of Bell‐type inequality violations using two‐ and four‐qubit Dicke states implemented on quantum computers are presented. Specifically, two methods for preparing four‐qubit Dicke states—gate‐based and statevector‐based—are compared, and their performance is assessed on two IBM superconducting quantum processors, ibm_kyiv and ibm_sherbrooke. In the two‐qubit scenario, a clear violation of the CHSH inequality is observed, with a maximum Bell parameter of 2.821±0.0019$2.821 \pm 0.0019$ achieved using M3 error mitigation, closely approaching the theoretical upper bound of 22$2\sqrt {2}$ . For the four‐qubit case, a Dicke‐state‐specific Bell‐type inequality is applied and a maximal violation of 2.607±0.029$2.607 \pm 0.029$ is reported without additional mitigation using the statevector‐based approach. These findings show that while error mitigation improves outcomes in gate‐based methods, the statevector‐based approach naturally provides higher fidelity with reduced noise. This work underscores the importance of state preparation strategies and noise management in exploring quantum correlations on current quantum computing platforms.