Identifiability and learning with quantum latent causes

Classical causal-inference theory (Pearl; Spirtes–Glymour–Scheines) uses directed acyclic graphs, interventions, and the do-calculus to extract cause–effect relations from correlations. A quantum version must handle noncommuting observables, latent quantum common causes, and possibly indefinite causal order — while still licensing identifiable causal conclusions.

What is known: A solid foundation exists for the fixed-order case. Quantum causal models on DAGs have been formulated (Costa–Shrapnel; Allen–Barrett–Horsman–Lee–Spekkens), with a quantum Markov condition and a resolution of Bell's theorem as a failure of classical common-cause explanation that quantum common causes can restore in some framings. Henson–Lal–Pusey and Wood–Spekkens analyzed which correlations admit classical causal explanation. Barrett–Lorenz–Oreshkov developed quantum causal models with a proper interventionist semantics and cyclic/indefinite-order generalizations.

Barrett–Lorenz–Oreshkov's quantum causal-model framework already supplies quantum analogues of all three do-calculus rules, as well as sound and complete d-separation for its conditional-independence notion. Thus a basic interventionist quantum formalism and quantum do-calculus are not missing.

Remaining inference targets must specify hidden-system dimensions, known or unknown graph, and accessible instruments: decide when a desired interventional statistic is determined by available data, when a proposed inference calculus is complete for that access model, and how sample complexity and robustness scale. Sound/complete d-separation is not automatically complete latent-cause identification. Physical realizability of indefinite order is tracked separately in F9.

Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.