# Violation of space-time Bell-CHSH inequality beyond Tsirelson bound via post selection and quantum cryptography

## TL;DR

This paper demonstrates that by incorporating context-dependent unitary evolutions and post selection into Bell-CHSH tests, it is possible to achieve maximal violations beyond Tsirelson's bound, leading to improved quantum cryptography protocols.

## Contribution

It introduces a method to violate the space-time Bell-CHSH inequality beyond Tsirelson's bound using post selection, expanding the understanding of quantum correlations.

## Key findings

- Maximal violation of space-time Bell-CHSH inequality up to 4.
- Tsirelson bound remains valid without context-dependent evolutions.
- Enhanced quantum key distribution protocol efficiency.

## Abstract

Here we show that, if we insert context dependent unitary evolutions (which can be achieved via post selection) into spatial (i.e., normal) Bell-CHSH test, then it is possible to violate space-time Bell-CHSH inequality maximally (i.e., up to $4$). However this does not contradict Tsirelson quantum bound ($2\sqrt{2}$), as the latter has been derived without taking into consideration context dependent unitary evolutions and/or post selection. As an important application, this leads to a more efficient quantum key distribution protocol.