# Causal Networks and Freedom of Choice in Bell's Theorem

arXiv: https://arxiv.org/abs/2105.05721 · HTML: https://mlsanity.com/paper/2105.05721/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 83 references that are in the map.
- First posted on arXiv 12 May 2021.

## Builds on (most cited first, 5 of 5)

- [The Inflation Technique for Causal Inference with Latent Variables](https://mlsanity.com/paper/1609.00672/) (2016)
- [Inferring latent structures via information inequalities](https://mlsanity.com/paper/1407.2256/) (2014)
- [Beyond Bell's Theorem II: Scenarios with arbitrary causal structure](https://mlsanity.com/paper/1404.4812/) (2014)
- [A unifying framework for relaxations of the causal assumptions in Bell's theorem](https://mlsanity.com/paper/1411.4648/) (2014)
- [Semidefinite tests for latent causal structures](https://mlsanity.com/paper/1701.00652/) (2017)

## Built on by (most cited first, 1 of 1)

- [Causal inference with imperfect instrumental variables](https://mlsanity.com/paper/2111.03029/) (2021)

## Abstract (arXiv)

Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum correlations with classical causal models. The violation of a Bell inequality, however, does not exclude classical models where some level of measurement dependence is allowed, that is, the choice made by observers can be correlated with the source generating the systems to be measured. Here, we show that the level of measurement dependence can be quantitatively upper bounded if we arrange the Bell test within a network. Furthermore, we also prove that these results can be adapted in order to derive nonlinear Bell inequalities for a large class of causal networks and to identify quantumly realizable correlations that violate them.