Violation of Qudit Mermin's Inequality and Its Application to Quantum Computing

ABSTRACT Mermin's inequality provides a fundamental test to verify the quantum nonlocality of multipartite Greenberger–Horne–Zeilinger (GHZ) states, by also serving as a key resource for measurement‐based quantum computing. While the theoretical foundation of Mermin's inequality test is well established for both qubit and qudit systems, the experimental validation for qudits remains elusive. In this work, we perform qudit Mermin's inequality test implemented on a qutrit (i.e., three‐level system) GHZ state, where the multipartition is achieved by deterministically entangling the time and frequency bins of a biphoton state via standard fiber‐optic components. The direct measurement of Mermin's operator yields an expectation value of 8.612(44), surpassing the bound of 6 for local realism by 59 standard deviations. We demonstrate the potential of the verified GHZ state for high‐dimensional quantum computing by utilizing the nonlocality results to compute a ternary logic function through non‐adaptive high‐dimensional measurement‐based quantum computation. Our scheme is readily scalable to higher dimensions without additional loss or modifications to the experimental setup.