Tight quantum bounds on causal effects for latent-variable DAGs

Determine tight quantum bounds on causal effects for specified causal DAGs with latent variables; ascertain when the NPA hierarchy is tight and whether the quantum-over-classical gap can be computed efficiently for DAGs used in econometrics.

Background

The paper maps Bell-type quantum bounds to causal DAGs with latent confounders and suggests using the NPA hierarchy to bound achievable quantum correlations in causal inference.

The authors pose the problem of characterizing tight quantum causal bounds, including conditions for NPA tightness and efficient computation of the quantum–classical gap for practical DAGs.

References

The unified framework raises several open questions that span the boundaries of quantum information, causal inference, and statistical computation. For a given causal DAG with latent variables, what are the tight quantum bounds on causal effects— that is, what causal effects are achievable if the latent confounders are quantum rather than classical? The NPA hierarchy gives an outer approximation; the question is when this approximation is tight, and whether the quantum-over-classical gap can be computed efficiently for DAGs arising in econometric applications.

— Bell's Inequality, Causal Bounds, and Quantum Bayesian Computation: A Unified Framework  (2603.28973 - Polson et al., 30 Mar 2026) in Section 7, Open Problems