# No Violation of Bell-CHSH Inequalities at Large Distances

**Authors:** Timofei Rusalev, Daniil Stepanenko, Igor Volovich  
**arXiv:** [2312.07499](https://arxiv.org/abs/2312.07499)  
**Date:** 2023-12-12  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2312.07499v1/

## Key points

- The usual derivation of the violation of Bell-type inequalities has limitations at large distances between detectors
- The dependence of the quantum mechanical wave function on space-time variables is not considered in this derivation
- Experiments using entangled photons obtained in SPDC show no violation of Bell-CHSH inequalities at large distances
- Lack of violation at large distances does not contradict observed violations at small distances
- Proposed experiment to study the dependence of quantum correlation function and Bell value on increasing distance between detectors
- Predicted that these quantities decrease inversely proportional to the increase in distance between detectors
- Research sheds light on unexplored aspect of entanglement and suggests refinement of understanding quantum mechanics for larger spatial scales
- Studying entangled photon behavior over different distances provides insights into how quantum correlations change with varying space-time variables.

## Summary

In their paper titled "No Violation of Bell-CHSH Inequalities at Large Distances," authors Timofei Rusalev, Daniil Stepanenko, and Igor Volovich address the limitations of the usual derivation of the violation of Bell-type inequalities. They argue that this derivation can only be applied to small distances between detectors and does not take into account the dependence of the quantum mechanical wave function on space-time variables. To investigate this further, the authors conduct experiments using entangled photons obtained in spontaneous parametric down-conversion (SPDC). They find that at large distances, there is actually no violation of the Bell-CHSH inequalities. This suggests that the initial entangled states become disentangled at large space-like distances. Importantly, this lack of violation at large distances does not contradict the observed violation of Bell inequalities at small distances between detectors. The authors propose an experiment to study the dependence of the quantum correlation function and Bell value on increasing distance between detectors. Based on their analysis, they predict that these quantities decrease inversely proportional to the increase in distance between the detectors. This research sheds light on a previously unexplored aspect of entanglement and highlights how our understanding of quantum mechanics may need to be refined when considering larger spatial scales. By studying entangled photon behavior over different distances, researchers can gain valuable insights into how quantum correlations change with varying space-time variables.