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

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. CONTENTS

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

“…This is because for every subnormalized state in one's GPT state space, it is physically possible to generate a normalized version of that state, e.g., by repeat-until-success preparation procedures [3]. 14 Such procedures are not possible within a multisource-multimeter scenario, which is why accessible GPT fragments may exclude the normalized counterparts of some subnormalized states in the fragment. One can see this in the example we depict in Fig.…”

“…which referred to it as the 'causality' condition. We do not endorse this terminology for the reasons espoused in Ref [14]10.…”

“…In fact, it is the slightly more general notion of Leibnizianity introduced in Ref [14],. but the distinction between the two will not be important here 7.…”

Possibility of causal loops without superluminal signalling -- a general framework

“…This would provide a general framework for causally modelling fine-tuned and cyclic non-classical causal models such that any post-intervention scenario can be completely specified by the original causal model. 18 Another observation made in Appendix C is that the presence of causal loops could allow us to distinguish between a faithful, non-classical explanations vs unfaithful classical explanations (e.g., using non-local hidden variables) of quantum correlations, which cannot be operationally distinguished otherwise. This suggests that it might be possible to operationally distinguish hidden variable interpretations of quantum theory such as Bohmian mechanics from inherently "quantum" interpretations, in the presence of causal loops.…”

“…This has fuelled several approaches for providing causal explanations to quantum and more general non-classical correlations. One approach is to develop genuinely non-classical causal models [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] that go beyond classical random variables and allow quantum or even post-quantum systems [19] to be causes. Other approaches suggest modifying the causal structure itself without necessarily considering non-classical causes in the causal model, such as allowing for additional causal influences that go outside the future light cone (e.g., non-local hidden variable theories [20]) or against the direction of time (retrocausality [21]).…”