Testing tripartite Mermin inequalities by spectral joint-measurements of qubits

It is well known that Bell inequality supporting the local realism can be violated in quantum mechanics. Numerous tests of such a violation have been demonstrated with bipartite entanglements. Using spectral jointmeasurements of the qubits, we here propose a scheme to test the tripartite Mermin inequality (a three-qubit Bell-type inequality) with three qubits dispersively-coupled to a driven cavity. First, we show how to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state by only one-step quantum operation. Then, spectral joint-measurements are introduced to directly confirm such a tripartite entanglement. Assisted by a series of single-qubit operations, these measurements are further utilized to test the Mermin inequality. The feasibility of the proposal is robustly demonstrated by the present numerical experiments.