Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Causal structures from entropic information: Geometry and novel
  scenarios   The fields of quantum non-locality in physics, and causal discovery in
machine learning, both face the problem of deciding whether observed data is
compatible with a presumed causal relationship between the variables (for
example a local hidden variable model). Traditionally, Bell inequalities have
been used to describe the restrictions imposed by causal structures on marginal
distributions. However, some structures give rise to non-convex constraints on
the accessible data, and it has recently been noted that linear inequalities on
the observable entropies capture these situations more naturally. In this
paper, we show the versatility of the entropic approach by greatly expanding
the set of scenarios for which entropic constraints are known. For the first
time, we treat Bell scenarios involving multiple parties and multiple
observables per party. Going beyond the usual Bell setup, we exhibit
inequalities for scenarios with extra conditional independence assumptions, as
well as a limited amount of shared randomness between the parties. Many of our
results are based on a geometric observation: Bell polytopes for two-outcome
measurements can be naturally imbedded into the convex cone of attainable
marginal entropies. Thus, any entropic inequality can be translated into one
valid for probabilities. In some situations the converse also holds, which
provides us with a rich source of candidate entropic inequalities.

26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th