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

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.

5 pages + appendix, v2: added references, v3: new title, added journal reference

References in corpus (7)

• Private Randomness Expansion With Untrusted Devices
• Beyond Bell's Theorem: Correlation Scenarios
• Information-Theoretic Implications of Quantum Causal Structures
• Theory-independent limits on correlations from generalised Bayesian networks
• Nonlinear Bell inequalities tailored for quantum networks
• Polynomial Bell inequalities
• Entropic nonsignaling correlations

Cited by in corpus (9)

• Why initial system-environment correlations do not imply the failure of complete positivity: a causal perspective
• Non-Shannon inequalities in the entropy vector approach to causal structures
• The entropic approach to causal correlations
• Indistinguishability of causal relations from limited marginals
• Quantum Causal Models
• Analysing causal structures in generalised probabilistic theories
• Computational tools for solving a marginal problem with applications in Bell non-locality and causal modeling
• Analysing causal structures using Tsallis entropies
• On the insufficiency of entropic inequalities for detecting non-classicality in the Bell causal structure