Its a Matter of Principle. Scientific Explanation in Information-Theoretic Reconstructions of Quantum Theory

The aim of this paper is to explore the ways in which Axiomatic Reconstructions of Quantum Theory in terms of Information-Theoretic principles (ARQITs) can contribute to explaining and understanding quantum phenomena, as well as to study their explanatory limitations. This is achieved in part by offering an account of the kind of explanation that axiomatic reconstructions of quantum theory provide, and re-evaluating the epistemic status of the program in light of this explanation. As illustrative cases studies, I take Clifton’s, Bub’s and Halvorson’s characterization theorem and Popescu’s and Rohrlich’s toy models, and their explanatory contribution with respect to quantum non-locality. On the one hand, I argue that ARQITs can aspire to provide genuine explanations of (some aspects of) quantum non-locality. On the other hand, I argue that such explanations cannot rule out a mechanical quantum theory.

💡 Research Summary

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The paper investigates how axiomatic reconstructions of quantum theory based on information‑theoretic principles (ARQIT) contribute to explaining quantum phenomena, especially non‑locality, and where their explanatory reach stops. It begins by rejecting the view that scientific explanation must be causal or mechanistic, arguing instead that explanations can be principle‑based and need not commit to any particular ontology. Drawing on Mark Steiner’s model of explanatory proofs, the author defines an explanation as showing how a phenomenon P depends on the essence S of a theory.

Two major case studies are examined. The first is the Clifton‑Bub‑Halvorson (CBH) theorem, which characterizes quantum theory within a C*‑algebraic framework using three “no‑go” information‑theoretic constraints: (i) no superluminal information transfer, (ii) no broadcasting (a generalisation of no‑cloning), and (iii) no unconditionally secure bit‑commitment. The paper shows that the first two constraints enforce two algebraic features: distinct systems’ algebras must commute (capturing no‑signalling) and each individual system’s algebra must be non‑commutative (capturing interference). When both hold, non‑local entangled states necessarily exist. The third constraint is argued to be redundant in the C*‑algebra setting but possibly needed in weaker algebraic structures (e.g., Segal algebras). The analysis also points out that the choice of C*‑algebras already excludes certain deterministic hidden‑variable theories, revealing a hidden ontological assumption in the reconstruction.

The second case study concerns partial reconstructions exemplified by Popescu‑Rohrlich (PR) boxes and related “toy” theories. Here the strategy is to build alternative “fantasy” theories that share some quantum principles while altering others, thereby probing which principle limits the amount of non‑locality observed in our world. By varying the no‑signalling, no‑broadcasting, and bit‑commitment constraints, one can generate theories that are more non‑local than quantum mechanics (maximally violating the Tsirelson bound) or less. This comparative exercise shows that the specific quantitative bound on quantum non‑locality (the Tsirelson limit) follows from a particular combination of information‑theoretic constraints, explaining why nature does not exhibit the extreme correlations of PR boxes.

From both studies the author concludes that ARQIT provides genuine explanations of “why” certain non‑local features exist and “why” they have the particular strength they do: the explanations are structural, showing how the chosen principles logically entail the phenomenon. However, these explanations stop short of addressing “how” the correlations are produced at the level of dynamics, measurement, or hidden variables. Consequently, ARQIT cannot rule out mechanical or ontological interpretations of quantum theory; it merely complements them.

The paper also tackles two philosophical claims that have been advanced by proponents of ARQIT. First, the claim that information is a fundamental ontological constituent of reality is rejected: information‑theoretic principles are formal tools, not metaphysical primitives. Second, the claim that traditional interpretations become explanatorily irrelevant is challenged; because ARQIT does not explain the mechanism of non‑locality, traditional realist or collapse‑based accounts remain necessary for a full understanding.

In the final section the author summarises that ARQIT offers a valuable explanatory layer—clarifying the logical dependence between information‑theoretic constraints and quantum phenomena—but it does not replace the need for ontological interpretations or for explanations that specify the underlying physical processes. The paper thus positions ARQIT as an important, though limited, component of the broader project of understanding quantum theory.