We consider 3‐qubit entangled pure states of the form α|000〉+β|111〉 and explore nonlocal correlations between the qubits by analyzing a Bell inequality belonging to the Mermin‐Klyshko (MK) set of N‐qubit inequalities. We find an expression for the maximum expectation value of the MK Bell operator and show that it does not increase smoothly with the amount of entanglement between the qubits. A subset of these tripartite entangled states does not violate the bound of 2 imposed by local hidden variable theories.

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