The resource theory of causal influence and knowledge of causal influence
5 affiliations
- 1Perimeter Institute for Theoretical Physics
- 2University of Gdańsk
- 3Uniwersytet Gdanski
- 4University College London
- 5University of Gdansk
Abstract

Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. A challenge to this is the fact that different functional causal models can induce the same conditional probability distribution over observed variables while encoding different amounts of causal influence. Motivated by this observation, we study the underlying functional mechanisms, including uncertainty over them, as meaningful objects in their own right and develop a resource-theoretic framework for quantifying causal influence and knowledge of causal influence.

We focus on the simplest nontrivial setting--- two variables that are causally ordered, meaning that the first has the potential to influence the second, without hidden confounding. 
First, we introduce the 
resource theory that directly quantifies causal influence of a functional dependence in this setting and show that the problem of deciding convertibility of resources and identifying a complete set of monotones has a relatively straightforward solution. 
Following this, we introduce the 
resource theory that arises naturally when one has uncertainty about the functional dependence. 
We describe a linear program for deciding the question of whether one resource (i.e., state of knowledge about the functional dependence) can be converted to another. Then, we focus on the case where the variables are binary. In this case, we identify a triple of monotones that are complete in the sense that they capture the partial order over the set of all resources, 
and we provide an interpretation of each.
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BibTeX
@article{ansanelli2026resource,
title = {{The resource theory of causal influence and knowledge of causal influence}},
author = {Marina Marciel Ansanelli and Beata Zjawin and David Schmid and Yìlè Yīng and John Harry Selby and Ciaran Gilligan-Lee and Ana Belen Sainz and Rob W Spekkens},
journal = {New Journal of Physics},
year = {2026},
month = oct,
doi = {10.1088/1367-2630/aeb568},
url = {https://iopscience.iop.org/article/10.1088/1367-2630/aeb568},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - The resource theory of causal influence and knowledge of causal influence
AU - Marina Marciel Ansanelli
AU - Beata Zjawin
AU - David Schmid
AU - Yìlè Yīng
AU - John Harry Selby
AU - Ciaran Gilligan-Lee
AU - Ana Belen Sainz
AU - Rob W Spekkens
PY - 2026
DA - 2026/10/16
JO - New Journal of Physics
DO - 10.1088/1367-2630/aeb568
UR - https://iopscience.iop.org/article/10.1088/1367-2630/aeb568
AB - 
Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. A challenge to this is the fact that different functional causal models can induce the same conditional probability distribution over observed variables while encoding different amounts of causal influence. Motivated by this observation, we study the underlying functional mechanisms, including uncertainty over them, as meaningful objects in their own right and develop a resource-theoretic framework for quantifying causal influence and knowledge of causal influence.

We focus on the simplest nontrivial setting--- two variables that are causally ordered, meaning that the first has the potential to influence the second, without hidden confounding. 
First, we introduce the 
resource theory that directly quantifies causal influence of a functional dependence in this setting and show that the problem of deciding convertibility of resources and identifying a complete set of monotones has a relatively straightforward solution. 
Following this, we introduce the 
resource theory that arises naturally when one has uncertainty about the functional dependence. 
We describe a linear program for deciding the question of whether one resource (i.e., state of knowledge about the functional dependence) can be converted to another. Then, we focus on the case where the variables are binary. In this case, we identify a triple of monotones that are complete in the sense that they capture the partial order over the set of all resources, 
and we provide an interpretation of each.
SN - 1367-2630
ER -