An explicit retrocausal model is used to analyze the general Wood-Spekkens argument [1] that any causal explanation of Bell-inequality violations must be unnaturally fine-tuned to avoid signaling. The no-signaling aspects of the model turn out to be robust under variation of the only free parameter, even as the probabilities deviate from standard quantum theory. The ultimate reason for this robustness is then traced to a symmetry assumed by the original model. A broader conclusion is that symmetry-based restrictions seem a natural and acceptable form of fine-tuning, not an unnatural model-rigging. And if the Wood-Spekkens argument is indicating the presence of hidden symmetries, this might even be interpreted as supporting time-symmetric retrocausal models.
An explicit retrocausal model is used to analyze the general Wood-Spekkens argument [1] that any causal explanation of Bell-inequality violations must be unnaturally fine-tuned to avoid signaling. The no-signaling aspects of the model turn out to be robust under variation of the only free parameter, even as the probabilities deviate from standard quantum theory. The ultimate reason for this robustness is then traced to a symmetry assumed by the original model. A broader conclusion is that symmetry-based restrictions seem a natural and acceptable form of fine-tuning, not an unnatural model-rigging. And if the Wood-Spekkens argument is indicating the presence of hidden symmetries, this might even be interpreted as supporting time-symmetric retrocausal models.
Wood and Spekkens ([2015]) argue that any causal model explaining the EPRB correlations and satisfying the no-signalling constraint must also violate the assumption that the model faithfully reproduces the statistical dependences and independences—a so-called ‘fine-tuning’ of the causal parameters. This includes, in particular, retrocausal explanations of the EPRB correlations. I consider this analysis with a view to enumerating the possible responses an advocate of retrocausal explanations might propose. I focus on the response of Näger ([2016]), who argues that the central ideas of causal explanations can be saved if one accepts the possibility of a stable fine-tuning of the causal parameters. I argue that in light of this view, a violation of faithfulness does not necessarily rule out retrocausal explanations of the EPRB correlations. However, when we consider a plausible retrocausal picture in some detail, it becomes clear that the causal modelling framework is not a natural arena for representing such an account of retrocausality. 1 Causal Models, Quantum Mechanics, and Faithfulness2 Fine-Tuning 2.1 Fine-tuning in a retrocausal model3 Possible Responses4 Quantum Causal Models and Retrocausality 4.1 A more detailed retrocausal account 4.2 A model of the EPRB probabilities 4.3 Mapping to a causal model5 Conclusion
Despite attempts to apply causal modeling techniques to quantum systems, Wood and Spekkens argue that any causal model purporting to explain quantum correlations must be fine tuned; it must violate the assumption of faithfulness. This paper is an attempt to undermine the reasonableness of the assumption of faithfulness in the quantum context. Employing a symmetry relation between an entangled quantum system and a “sideways” quantum system consisting of a single photon passing sequentially through two polarizers, I argue that Wood and Spekkens’s analysis applies equally to this sideways system also. As a result, we must either reject a causal explanation in this single photon system, or the sideways system must be fine tuned. If the latter, a violation of faithfulness in the ordinary entangled system may be more tolerable than first thought. Thus, extending the classical “no fine-tuning” principle of parsimony to the quantum realm may be too hasty.
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.
An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms , the purpose of which is to infer the causal relations that hold among a set of variables from the correlations that these exhibit . We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles.
Causal-model arguments establish that a classical causal model reproducing Bell correlations while exhibiting no-signalling must be unfaithful: its no-signalling independences are not entailed by d-separation in the causal graph. Applied to time-symmetric, retrocausal, and all-at-once models, this is the fine-tuning objection. The resulting debate has largely concerned whether faithfulness is the appropriate norm, without a criterion for deciding particular cases or an associated measurement.This paper supplies a proposed criterion and establishes a precise symmetry result for the balanced binary singlet sector. If a nonnegative 2×2 compatibility table has the simultaneous-outcome-flip symmetry m++=m−−,m+−=m−+, then every common scalar entrywise map mxy⟼f(mxy) with nonnegative output and nonzero normalization preserves uniform local marginals. No monotonicity, continuity, differentiability, or power-law assumption is required. Within two-qubit quantum kinematics with ideal analyzer projectors, joint rotational invariance and perfect same-axis anticorrelation force the singlet state and hence this pairing symmetry. The theorem establishes robustness relative to the symmetry-restricted deformation class; it does not confer causal faithfulness or robustness against arbitrary symmetry-breaking cellwise perturbations.The same singlet-plus-common-map structure has a deformation-independent surplus consequence: Ef(π−Δ)=−Ef(Δ),Ef(π/2)=0. These angular identities are distinct from no-signalling and can fail experimentally. They provide the surplus consequence required by the proposed criterion in the balanced sector.A separate constant-flux completion law predicts an exactly flat ideal joint completion rate. We compare it with a Bell-local sign--cosine model followed by a joint two-bin selection rule. The pointwise maximal acceptance envelope for reproducing the singlet correlator has symmetric minima Z∗≃0.878567 near 46.44∘ and 133.56∘. A flat calibrated joint acceptance rate above this value excludes that two-bin class. More generally, total variation gives Sobs≤min{4,2+2∑q∈Q(1−Zq)}, so a flat rate above 45−2≃0.896447 excludes every Bell-local measurement-independent selection model covered by this bound when Sobs=22.Finally, an exact eight-state reconstruction of a published post-processing model has acceptance rate 3/4 in every setting context while attaining the algebraic CHSH value 4. Its accepted laws satisfy ΔQ=1,DQ=31, saturating both the selection-inflation lower bounds and the upper bounds permitted by the absolute rate. Thus rate flatness is not a certificate of fair sampling, although the absolute rate remains quantitatively useful. The quantity requiring structural certification is the conditional acceptance function, or a sufficient experimentally accessible proxy for it.
Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and 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-signalling 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 space-like separated systems, and manifests already in scenarios involving single systems.