Classical Causal Models for Bell and Kochen-Specker Inequality Violations Require Fine-Tuning

Abstract

Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and they are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure. Contextuality, on the other hand, is on a more controversial foundation. In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality. First, I show that Bell inequalities can be derived solely from the assumptions of no signaling and no fine-tuning of the causal model. This removes two extra assumptions from a recent result from Wood and Spekkens and, remarkably, does not require any assumption related to independence of measurement settings-unlike all other derivations of Bell inequalities. I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning. Thus, the quantum violation of classical causality goes beyond the case of spacelike-separated systems and already manifests in scenarios involving single systems.

Relating causal and probabilistic approaches to contextuality

“…The present article proves an affirmative answer to this question, based on a characterization of contextuality recently advanced by Cavalcanti [7] in terms of probabilistic causal models. Probabilistic causal models are widely used in statistics, computer science, machine learning, and psychology and are well suited for situations involving stochastic latent structure [24,27].…”

“…First, it maintains the standard interpretation of contextuality as the impossibility of explaining a system classically, meaning with a hidden-variables theory in which measurements that were not made are nevertheless welldefined [19]. Second, it distinguishes direct influence, a property of the theoretical data-generating process, from inconsistent connectedness, a property of the data distribution [7]. Consequently, third, it provides a formalism for expressing how an observable might directly depend on context, thus enabling potential extensions wherein theoretical assumptions regarding the physical system impose additional constraints on this dependence.…”

“…However, we suggest the modelbased approach offers two conceptual advantages. First, the model-based approach emphasizes the ontological distinction between the measurements M c q as physical events, and the random variables Fq as theoretical constructs meant to explain those physical events (when taken together with the other components of M) [7]. Second, a canonical causal model contains explicit causal structure via the latent variable Λ, which enables formal definition of direct influences of C on Fq (see Section 4).…”

Experimental Non-Violation of the Bell Inequality

“…However, unlike T , T is an unrealistically fine-tuned theory [23,24], since rationals and irrationals lie arbitrarily close to each other on the real line with respect to the standard Euclidean metric. The notion that distances in physics should be necessarily described by the Euclidean metric is a deeply held intuition, since almost the first thing we learn as babies is a sense of spatial awareness (for the baby to get its hand close to a colourful toy, it has to learn to equate closeness with smallness of Euclidean distance).…”

Unifying framework for spatial and temporal quantum correlations

“…A general principle advocated for Bell nonlocality [43] and noncontextuality [44], and to probe temporal nonclassicality [45], is "no fine-tuning": all causal links should manifest in corresponding correlations.…”