Unexpected consequences of Post-Quantum theories in the graph-theoretical approach to correlations

TL;DR

This paper investigates how the exclusivity principle constrains post-quantum correlations, showing that if all quantum behaviors exist, then no post-quantum behaviors can occur, offering new insights into quantum correlation structures.

Contribution

It proves that the exclusivity principle limits post-quantum correlations to the antiblocking set, extending previous results to broader scenarios and deepening understanding of quantum correlation boundaries.

Findings

EP restricts correlations to the antiblocking set given complementary experiment data

If all quantum behaviors are possible, postquantum behaviors are excluded by EP

Provides a generalized framework for quantum correlation limitations

Abstract

This work explores the implications of the exclusivity principle (EP) in the context of quantum and postquantum correlations. We first establish a key technical result demonstrating that given the set of correlations for a complementary experiment, the EP restricts the maximum set of correlations for the original experiment to the antiblocking set. Based on it, we can prove our central result: if all quantum behaviors are accessible in Nature, the EP guarantees that no postquantum behaviors can be realized. This can be seen as a generalization of the result of B. Amaral et al. [Phys. Rev. A 89, 030101(R) (2014)], to a wider range of scenarios. It also provides novel insights into the structure of quantum correlations and their limitations.