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The experimental test of Bell's inequality is mainly focused onClauser-Horne-Shimony-Holt (CHSH) form, which provides a quantitative bound,while little attention has been pained on the violation of Wigner inequality(WI). Based on the spin coherent state quantum probability statistics we in thepresent paper extend the WI and its violation to arbitrary two-spin entangledstates with antiparallel and parallel spin-polarizations. The local part ofdensity operator gives rise to the WI while the violation is a direct result ofnon-local interference between two components of the entangled states. TheWigner measuring outcome correlation denoted by $W$ is always less than or atmost equal to zero for the local realist model ($% W_{lc_{{}}}\leq 0$)regardless of the specific initial state. On the other hand the violation of\WI is characterized by any positive value of $W$, which possesses a maximumviolation bound $W_{\max }$ $=1/2$. We conclude that the WI is equallyconvenient for the experimental test of violation by the quantum entanglement.

Maximum violation of Wigner inequality for two-spin entangled states with parallel and antiparallel polarizations