Unscrambling the omelette of causation and inference: The framework of causal-inferential theories

TL;DR

This paper introduces a formal framework combining causal influences and inference theories to clarify realist and operational accounts in quantum theory, offering new perspectives on no-go theorems and quantum realism.

Contribution

It develops a process-theoretic formalism for causal-inferential theories, providing a novel characterization of assumptions in quantum no-go theorems and proposing a way to define quantum-specific notions of realism.

Findings

Recasting operational and realist theories clarifies their differences.

Characterization of assumptions behind Bell's locality and noncontextuality theorems.

Proposal of axioms for a quantum-specific notion of realism.

Abstract

Using a process-theoretic formalism, we introduce the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. Recasting the notions of operational and realist theories in this mold clarifies what a realist account of an experiment offers beyond an operational account. It also yields a novel characterization of the assumptions and implications of standard no-go theorems for realist representations of operational quantum theory, namely, those based on Bell's notion of locality and those based on generalized noncontextuality. Moreover, our process-theoretic characterization of generalised noncontextuality is shown to be implied by an even more natural principle which we term Leibnizianity. Most strikingly, our framework offers a way forward in a research program that seeks to circumvent these no-go results. Specifically, we argue that if one can identify axioms for a realist causal-inferential theory such that the notions of causation and inference can differ from their conventional (classical) interpretations, then one has the means of defining an intrinsically quantum notion of realism, and thereby a realist representation of operational quantum theory that salvages the spirit of locality and of noncontextuality.