Witnessing Non-Classicality in a Simple Causal Structure with Three Observable Variables

TL;DR

This paper investigates a lesser-studied causal structure with three observable variables, called the Evans scenario, analyzing its potential for quantum non-classicality and introducing new computational tools for its study.

Contribution

It introduces new methods for analyzing the Evans causal structure and demonstrates that post-quantum correlations violate classical constraints in this scenario.

Findings

Post-quantum correlations violate classical constraints in the Evans scenario.

New computational tools are developed for analyzing complex causal structures.

The Evans scenario is shown to be a promising avenue for understanding quantum non-classicality.

Abstract

Seen from the modern lens of causal inference, Bell's theorem is nothing else than the proof that a specific classical causal model cannot explain quantum correlations. It is thus natural to move beyond Bell's paradigmatic scenario and consider different causal structures. For the specific case of three observable variables, it is known that there are three non-trivial causal networks. Two of those, are known to give rise to quantum non-classicality: the instrumental and the triangle scenarios. Here we analyze the third and remaining one, which we name the Evans scenario, akin to the causal structure underlying the entanglement-swapping experiment. We prove a number of results about this elusive scenario and introduce new and efficient computational tools for its analysis that also can be adapted to deal with more general causal structures. We do not solve its main open problem -- whether quantum non-classical correlations can arise from it -- but give a significant step in this direction by proving that post-quantum correlations, analogous to the paradigmatic Popescu-Rohrlich box, do violate the constraints imposed by a classical description of Evans causal structure.