English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A causal structure is a relationship between observed variables that ingeneral restricts the possible correlations between them. This relationship canbe mediated by unobserved systems, modelled by random variables in theclassical case or joint quantum systems in the quantum case. One way todifferentiate between the correlations realisable by two different causalstructures is to use entropy vectors, i.e., vectors whose components correspondto the entropies of each subset of the observed variables. To date, thestarting point for deriving entropic constraints within causal structures arethe so-called Shannon inequalities (positivity of entropy, conditional entropyand conditional mutual information). In the present work we investigate whathappens when non-Shannon entropic inequalities are included as well. We showthat in general these lead to tighter outer approximations of the set ofrealisable entropy vectors and hence enable a sharper distinction of differentcausal structures. Since non-Shannon inequalities can only be applied amongstclassical variables, it might be expected that their use enables an entropicdistinction between classical and quantum causal structures. However, thisremains an open question. We also introduce techniques for deriving innerapproximations to the allowed sets of entropy vectors for a given causalstructure. These are useful for proving tightness of outer approximations orfor finding interesting regions of entropy space. We illustrate thesetechniques in several scenarios, including the triangle causal structure.

Non-Shannon inequalities in the entropy vector approach to causal structures