Spin-parity effect in violation of bell's inequalities for entangled states of parallel polarization

TL;DR

This paper extends Bell inequalities to bipartite-entangled states with parallel polarization, revealing a spin parity effect where violations occur only for half-integer spins due to Berry-phase influences.

Contribution

It generalizes Bell inequalities to parallel polarization states and uncovers the persistent spin parity effect, linking violations to Berry-phase effects in half-integer spins.

Findings

Violations occur only for half-integer spins due to Berry-phase effects.

Integer spins always satisfy Bell inequalities, showing no violation.

The spin parity effect persists in parallel polarization configurations.

Abstract

Bell inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while, the inequality for- mulated by Clauser-Horne-Shimony-Holt remains not changed. The violation of BIs indeed resulted from the quantum non-local correlation for spin-1=2 case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two spins. The spin parity effect originally demonstrated with the antiparallel spin-polarizations (Mod. Phys. Lett. B28, 145004) still exists for the parallel case. The quantum non-locality does not lead to the violation for integer spins due to the cancellation of non-local interference effects by the quantum statistical-average. Again the violation of BIs seems a result of the measurement induced nontrivial Berry-phase for half-integer spins.