Informational Pruning as a Third Path: Final-State Constraints between Consistent Quantum Causes and Quantum Causal Models

Abstract

Two recent programs offer competing accounts of quantum causation. Griffiths' Consistent Quantum Causes grounds causal reasoning in the Consistent Histories formalism, treating stochastic quantum time development and noncommuting projectors as the proper foundation for a Pearl-style directed acyclic graph representation. The Costa–Shrapnel Quantum Causal Models program takes the process-matrix formalism as its starting point, generalizing classical interventionist causal discovery to the quantum domain and extending naturally to indefinite causal order. Both programs assume that causal structure is fixed by an initial condition together with forward dynamics. Neither addresses what happens when admissibility is conditioned at both temporal boundaries. In this paper, I argue that final-state-constrained history ensembles, and the informational pruning they induce, provide a third vantage point from which to compare these two programs. I do not claim to resolve the Griffiths–QCM disagreement, nor to construct a new quantum causal formalism from scratch. The more limited claim is that once admissibility is globally filtered by an initial and a final boundary condition, the question of which coarse-grained histories carry the effective causal and computational structure of the process is reframed. The Hartle–Craig rank-product theorem supplies the formal backbone: imposing a final-state projector with rank r_ω restricts the admissible-history family to at most r_α·r_ω nonzero-probability histories, where r_α is the initial-state rank. I illustrate this with the three-box paradox, treated as a joint Consistent Histories and process-matrix scenario under final-state conditioning. I also suggest that an explainability stance, drawn in a methodological sense from explainable artificial intelligence, is useful for asking which admissible histories do the explanatory work under a given endpoint class. I conclude that informational pruning offers a coherent third path that is neither a competitor to Griffiths' approach nor an extension of process-matrix interventionism, but a complementary perspective that sharpens what each program leaves implicit.

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