# Structure of quantum and classical implementations of Popescu-Rohrlich box

## TL;DR

This paper explores how Popescu-Rohrlich boxes can be implemented using quantum and classical channels, revealing structural similarities and properties like entanglement-breaking in quantum cases.

## Contribution

It provides a unified construction approach for PR-box implementations in quantum and classical frameworks, highlighting their structural features and quantum channel characteristics.

## Key findings

- Quantum channels that maximize CHSH violation are entanglement-breaking.
- All such quantum channels share a block-diagonal structure.
- The constructions are inspired by general probabilistic theories and the square state space model.

## Abstract

We construct implementations of the PR-box using quantum and classical channels as state spaces. In both cases our constructions are very similar and they share the same idea taken from general probabilistic theories and the square state space model. We construct all quantum qubit channels that maximally violate a given CHSH inequality, we show that they all are entanglement-breaking channels, that they have certain block-diagonal structure and we present some examples of such channels.