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

David Schmid; John H. Selby; Robert W. Spekkens

Home/Archive/arXiv

arXiv · 2009.03297

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

David Schmid·John H. Selby·Robert W. Spekkens

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

David Schmid, John H. Selby, Robert W. Spekkens. 2021-05-19. Unscrambling the omelette of causation and inference: The framework of causal-inferential theories. https://arxiv.org/abs/2009.03297

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bounded information as a foundation for quantum theory

The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics - that the information carried by a system is limited - and, from this principle, to construct the foundations of quantum theory. In our discussion, we also introduce a second important hypothesis: if a measurement closely approximates an ideal one in terms of experimental precision, the information it provides about a physical system is independent of the measurement method and, specifically, of the system's physical quantities being measured. This principle can be expressed in terms of metric properties of a manifold whose points represent the state of the system. These and other reasonable hypotheses provide the foundation for a framework of quantum reconstruction. The theory presented in this paper is based on a description of physical systems in terms of their statistical properties, specifically statistical parameters, and focuses on the study of estimators for these parameters. To achieve the goal of quantum reconstruction, a divide-and-conquer approach is employed, wherein the space of two discrete conjugate Hamiltonian variables is partitioned into a binary tree of nested sets. This approach naturally leads to the reconstruction of the linear and probabilistic structure of quantum mechanics.

quant-ph↗

arXiv2026

Reducibility of native weighted graphs on Rydberg Arrays

We investigate the classical reducibility of random unit-disk graph (UDG) instances of the maximum independent set (MIS) and maximum weighted independent set (MWIS) problems, which can be natively realised in Rydberg atom quantum processors. Using state-of-the-art kernelisation techniques, we systematically probe how far classical preprocessing can simplify such native optimisation problems of varying size and connectivity. While many small or sparse instances can be fully reduced, dense graphs often retain finite irreducible kernels even after extensive reductions. Introducing vertex weights tends to increase reducibility, whereas extending the interaction range in the underlying UDG connectivity suppresses the reduction efficiency. By exploring where classical reductions cease to be effective, we aim to delineate the regime of problem instances that remain computationally demanding - those most relevant for testing and benchmarking near-term quantum optimisation hardware. We find that for the remaining finite kernels, quantum execution would require non-native embeddings with substantial resource overheads, suggesting that directly running native instances may be more practical than embedding a reduced kernel.

quant-ph↗

arXiv2026

When Complementary Measurements Count the Same Classical Bit Twice: Counterexamples to CQC, ECQC, and Complementarity-Based Certification

Mutually unbiased measurements are commonly expected to expose independent facets of a quantum state: a correlation that is classical in one basis should disappear in a complementary basis. In higher dimensions, however, this intuition becomes particularly subtle because correlations recovered in different settings need not represent different information. To expose this loophole, we propose a two-branch classical null test: before the setting is chosen, a shared bit selects one of two orthogonal product preparations, producing a rank-two classical--classical state, and the candidate protocol then runs unchanged. Different settings can read the same bit through different outcome patterns. This two-branch classical architecture disproves the complementary-quantum correlation (CQC) conjecture in every dimension $d\geq3$. A distinct rank-two classical--classical state disproves its complete-basis extension (ECQC) at $d=7$, with an overrun that grows without bound along prime dimensions. Its qutrit CQC instance also gives classical false positives for a proposed quantum-correlation measure and a proposed one-sided semi-device-independent steering criterion, and refutes a conditional-probability conjecture. The failures identify the missing requirement: information read in different settings must be nonredundant. In experiments and applications, the same low-overhead architecture can serve as a calibration test before a multibasis score is assigned quantum meaning.

quant-ph↗