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

TL;DR

This paper extends the Wigner inequality to arbitrary two-spin entangled states with parallel and antiparallel polarizations, demonstrating its maximum violation bound and potential for experimental tests of quantum entanglement.

Contribution

It introduces a generalized form of Wigner inequality for two-spin states and identifies its maximum violation bound, enhancing tools for testing quantum entanglement.

Findings

Wigner inequality violation characterized by positive W values.

Maximum violation bound of Wigner inequality is 1/2.

Wigner inequality is practical for experimental entanglement tests.

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 pained on 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 non-local interference between two components of the entangled states. The Wigner measuring outcome correlation denoted by $W$ is always less than or at most 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 maximum violation bound $W_{\max }$ $=1/2$. We conclude that the WI is equally convenient for the experimental test of violation by the quantum entanglement.