Quantum Non-localities and Correlation-Measurement-Induced Berry Phases for Spin-Singlet States

TL;DR

This paper analytically explores how quantum non-local correlations in spin-singlet states relate to Bell inequality violations, highlighting the role of Berry phases in half-integer spins and suggesting experimental tests with entangled photons.

Contribution

It provides a theoretical analysis linking Berry phases to Bell inequality violations in half-integer spin singlets, extending understanding of quantum non-locality.

Findings

Bell violations occur in spin-1/2 singlets due to non-local correlations.

Spin-1 singlets always satisfy Bell inequalities, showing no violation.

Berry phases enable Bell violations in half-integer spins.

Abstract

We in this Letter derive analytic formulas of Bell correlations in terms of quantum probability statistics under the assumption of measuring outcome-independence. For a spin-1/2 singlet state we find analytically that the violations of Bell-type inequalities are really related to the quantum non-local correlations. However, the Bell and Clauser-Horne-Shimony-Holt (CHSH) inequalities are always satisfied for the spin-1 singlet states. More generally the quantum non-locality does not lead to the violation of Bell and CHSH inequalities for the integer-spin singlet since the non-local interference effects cancel each other by the quantum statistical-average. Such a cancellation no longer exists for the half-integer spin singlets due to the nontrivial Berry phase, and thus the relevant Bell-type inequalities can be violated. Specifically, our generic observations can be experimentally tested with the entangled photon-pairs. Our arguments are based on the spin-singlet states, but could be generalized to other bipartite quantum states.