Hardy’s non-locality in four-qubit state

Hardy’s non-locality provides a proof of the incompatibility between quantum mechanics and local realism without using Bell inequalities. While this argument has been extensively studied for two- and three-qubit systems, a detailed analysis of the four-qubit case is still lacking. In this work, we investigate Hardy’s non-locality for a four-qubit system within the standard two-setting framework. We explicitly construct the entangled state satisfying the Hardy conditions and determine the measurement settings that maximize the success probability. • We present an explicit analytical construction of a four-qubit Hardy state together with the corresponding projective measurement settings. • The maximum Hardy success probability for four qubits is found to be 0.143, exceeding the values obtained in the two- and three-qubit cases. • The resulting state is non-maximally entangled and exhibits genuine multipartite quantum correlations.