This preprint (arXiv:2603.28973v1, not peer-reviewed) presents a purely theoretical mathematical unification rather than new experimental data. It demonstrates that the polytope of correlations forbidden by Bell's inequality is identical to the marginal compatibility polytope studied in causal inference. There is no sample size as this is not an empirical study; the 'methodology' consists of showing structural equivalence between models using probability theory, linear programming, and semidefinite programming.

Bell's inequality, introduced in 1964, limits how strongly two distant particles can correlate their measurements if the world is local and realistic. Quantum mechanics exceeds this limit, reaching Tsirelson's bound of 2√2 for the CHSH inequality. The paper reveals this same boundary appears in econometrics and statistics when researchers attempt to infer causal effects despite hidden confounding variables.

Using Fine's theorem as the pivot, the authors prove that the instrumental variable model in causal inference is mathematically identical to the Bell local-hidden-variable model. The 'instrument' plays the role of the measurement choice, while the latent confounder is the hidden variable λ. This yields identical inequalities: the instrumental inequality is the CHSH inequality in disguise, and the Balke-Pearl bounds are facets of the same polytope.

The work further connects these ideas to algorithmic (Kolmogorov complexity) and entropic versions of Bell inequalities, the NPA hierarchy for approximating quantum correlations, and the MIP*=RE result showing that certain quantum problems are undecidable. It then links non-commutativity—the mathematical feature enabling Bell violations—to quantum Bayesian computation, where the Born rule acts like a non-commutative Bayes rule, offering polynomial speedups for posterior inference in certain models.

Original coverage of these topics has typically treated quantum foundations, causal econometrics, and quantum computing as separate silos. What this paper identifies that others missed is the shared polytope geometry governing all three. Previous literature on quantum causality (e.g., using causal models for quantum processes) rarely makes the direct connection to Balke-Pearl bounds or Tian-Pearl probabilities of causation.

Synthesizing this with related sources, the 2020 MIP*=RE proof (arXiv:2001.04383) by Ji, Natarajan, Vidick and others established that quantum entanglement leads to undecidability in interactive proofs, while Judea Pearl's foundational 1995 paper on causal diagrams provided the language for bounding effects under latent confounding. Together they reveal a recurring pattern: constraints on joint distributions under partial information produce the same geometric structures whether the setting is physics, economics, or computation.

Philosophically, this unification challenges classical notions of causality and reality. If the same non-commutativity that violates Bell also accelerates Bayesian updating, then quantum mechanics may not be an isolated peculiarity of microscopic particles but a deeper feature of how information and causation combine. Limitations include the purely theoretical nature with no numerical simulations or hardware implementations; real-world noise and finite data may weaken these connections. The framework suggests new algorithms for quantum causal inference but stops short of providing them.

This lens reframes quantum foundations as part of a broader science of inference under constraints, with potential impact on causal AI, econometric modeling, and quantum algorithm design.