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

Abstract

The experimental test of Bell’s inequality is mainly focused on Clauser–Horne–Shimony–Holt (CHSH) form, which provides a quantitative bound, while little attention has been paid to the violation of Wigner inequality (WI). Based on the spin coherent state quantum probability statistics, we in the present paper extend the WI and its violation to arbitrary two-spin entangled states with antiparallel and parallel spin-polarizations. The local part of density operator gives rise to the WI while the violation is a direct result of nonlocal interference between two components of the entangled states. The Wigner measuring outcome correlation denoted by [Formula: see text] is always less than or at most equal to zero for the local realist model ([Formula: see text]) regardless of the specific initial state. On the other hand, the violation of WI is characterized by any positive value of [Formula: see text], which possesses a maximum violation bound [Formula: see text] [Formula: see text]. We conclude that the WI is equally convenient for the experimental test of violation by the quantum entanglement.