# Maximal violation of Bell inequalities under local filtering

## TL;DR

This paper analyzes how local filtering operations can enhance the detection of quantum non-locality by maximizing violations of Bell inequalities, revealing states that are non-local only after filtering.

## Contribution

It introduces an analytical method to compute maximal Bell inequality violations under local filtering for two-qubit systems, highlighting cases where non-locality is revealed post-filtering.

## Key findings

- Local filtering can increase Bell inequality violations.
- Some states exhibit non-locality only after filtering.
- The method applies to general two-qubit systems.

## Abstract

We investigate the behavior of the maximal violations of the CHSH inequality and V$\grave{e}$rtesi's inequality under the local filtering operations. An analytical method has been presented for general two-qubit systems to compute the maximal violation of the CHSH inequality and the lower bound of the maximal violation of V$\acute{e}$rtesi's inequality over the local filtering operations. We show by examples that there exist quantum states whose non-locality can be revealed after local filtering operation by the V$\acute{e}$rtesi's inequality instead of the CHSH inequality.