Inability of the entropy vector method to certify nonclassicality in linelike causal structures

TL;DR

This paper investigates whether the entropy vector method can certify nonclassicality in linelike causal structures, finding it insufficient and highlighting the need for alternative approaches.

Contribution

It demonstrates that the entropy vector method cannot certify nonclassicality in certain causal structures, including bipartite Bell scenarios, revealing limitations of this approach.

Findings

Entropy vectors do not certify nonclassicality in the studied structures.

Nonclassical correlations exist despite the entropy vector method's limitations.

The results suggest the need for alternative methods to understand quantum causality.

Abstract

Bell's theorem shows that our intuitive understanding of causation must be overturned in light of quantum correlations. Nevertheless, quantum mechanics does not permit signalling and hence a notion of cause remains. Understanding this notion is not only important at a fundamental level, but also for technological applications such as key distribution and randomness expansion. It has recently been shown that a useful way to decide which classical causal structures could give rise to a given set of correlations is to use entropy vectors. These are vectors whose components are the entropies of all subsets of the observed variables in the causal structure. The entropy vector method employs causal relationships among the variables to restrict the set of possible entropy vectors. Here, we consider whether the same approach can lead to useful certificates of non-classicality within a given causal structure. Surprisingly, we find that for a family of causal structures that include the usual bipartite Bell structure they do not. For all members of this family, no function of the entropies of the observed variables gives such a certificate, in spite of the existence of nonclassical correlations. It is therefore necessary to look beyond entropy vectors to understand cause from a quantum perspective.