# A Logical Proof of Quantum Correlations Requiring Entanglement Measurements

## TL;DR

This paper introduces a logical proof demonstrating quantum correlations that require entanglement, using graph theory and the global exclusivity principle, achieving a high success probability and connecting to well-known quantum inequalities.

## Contribution

It presents a novel logical proof of quantum correlations that necessitate entanglement measurements, with a new paradox related to Hardy, KCBS, and CHSH inequalities.

## Key findings

- Achieved $p_{Hardy} \,\approx\, 0.167$, the highest for similar systems.
- Connected logical proofs to graph theory and the global exclusivity principle.
- Built a paradox based on the CHSH inequality.

## Abstract

We present a logical type of proof of contextuality for a two-qubit state. We formulate a paradox that cannot be verified by a two-qubit system with local measurements while it is possible by using entanglement measurements. With our scheme we achieve $p_{\rm Hardy} \approx 0.167$, which is the highest probability obtained for a system of similar dimension. Our approach uses graph theory and the global exclusivity principle to give an interpretation of logical type of proofs of quantum correlations. We review the Hardy paradox and find connection to the KCBS inequality. We apply the same method to build a paradox based the CHSH inequality.