Deutsch and Marletto's constructor theory of information (2015) formulates a non-probabilistic theory of information purely in terms of which physical transformations are possible and which are impossible, and conjectures nine principles (I-IX) as exact laws of physics governing information media, showing that quantum-theoretic information is one instance of 'superinformation'. The principles are conjectures whose scope is not established: it is unknown for which subsidiary theories (the dynamical theories the principles constrain) principles III-IX hold, the preparation and composition principles VI-VII assume unlimited resources and are violated in cosmologies with finite computational resources, and the class of superinformation media admitted by the principles is uncharacterized, so it is open whether quantum theory is the only physical realization of superinformation or whether post-quantum theories can instantiate it. Later constructor-theoretic work has substantially developed the probability and experimental-testing components of the original question, but it has not closed this theoretical core, which therefore remains open.

Background

Constructor theory, proposed by David Deutsch in 2013, is a meta-theoretic reformulation of physics in which fundamental laws are 'principles' — statements about which physical transformations are possible and which are impossible — rather than predictions computed from initial conditions and laws of motion. A 'constructor' is the abstract entity that causes a transformation while remaining capable of causing it again; the systems transformed are 'substrates', each characterized at a time by an 'attribute' (a set of its possible states). A 'task' is the abstract specification of which input attributes are to be converted into which output attributes. Theories about the remaining, conventional laws of physics are called 'subsidiary theories'; principles are laws that constrain subsidiary theories rather than the behaviour of physical objects directly, and they are testable only indirectly: a principle is refuted if a subsidiary law violating it survives experimental test.

Deutsch and Marletto's 'Constructor theory of information' (2015) defines computation, measurement, and information in these terms. An 'information medium' is a substrate with an information variable — a set of attributes on which all permutation tasks and the cloning task are possible; 'measurement' is a task whose output carries information about the input attribute. The paper's central move is to conjecture principles I-IX as exact, subsidiary-theory-independent laws about information. The load-bearing ones for this problem are: the interoperability principle III (combining two information media yields an information medium with the Cartesian product variable S1×S2S_1 \times S_2, which requires specific interactions to exist in nature — it would, for instance, rule out dark-matter sectors whose media cannot exchange information with normal matter); the distinguishability principles IV and V (pairwise distinguishability of attributes implies distinguishability of the variable, and attributes distinguishable from a given attribute form a distinguishable set); the preparation principle VI (any number of instances of any information medium, in any information-instantiating attribute, is preparable from 'generic resources', i.e. naturally occurring unlimited substrates); the composition principle VII (every regular network of possible tasks is itself a possible task — an assumption of unlimited resources for information processing); the consistency-of-measurement principle VIII (all measurers of a variable are measurers of a single unique 'observable'); and the ensemble distinguishability principle IX (any two disjoint, intrinsic attributes are distinguishable given unlimited copies of the substrate). Notably, the framework is deliberately non-probabilistic: principle I requires all subsidiary theories to be expressible in terms of possible and impossible tasks, which rules out fundamentally stochastic laws, so probability can at most be an emergent description.

A 'superinformation medium' is then defined as an information medium with at least two information observables (an 'observable' being a set of mutually disjoint attributes of the substrate that can be measured) containing only mutually disjoint attributes whose union is not an information observable — that is, a medium on which certain naturally defined cloning or permutation tasks are impossible. The paper proves that quantum theory is an instance of superinformation: the impossibility of cloning, the non-distinguishability of some states, the irreducible disturbance and unpredictability of measurement, and entanglement (locally inaccessible information) all follow from this single prohibition. Two caveats stated by the authors frame the open problem. First, universality is not established: the paper notes that none of its results depends on principles IV-VIII holding universally in nature — they could hold only 'for a special class of substrates' — and principles III and IX are likewise conjectures; in particular VI and VII are violated in cosmological models with finite resources for computation, a limitation the authors acknowledge but set aside. Second, the theory is expressly not a derivation of quantum theory: it is a framework in which information under a broad range of theories, including 'post-quantum' theories, could be understood provided they obey the principles. Whether quantum theory is the unique physical realization of superinformation, and what other realizations the principles admit, is therefore not settled by the source; subsequent constructor-theoretic work (Marletto's constructor theory of probability, 2016) explicitly leaves open which concrete 'superinformation theories' exist.

Problem Statement

Determine the physical scope and the model class of the conjectured principles of the constructor theory of information.

(1) Universality and scope. For which subsidiary theories — the dynamical theories that the principles constrain — do the conjectured information principles III-IX hold? The interoperability principle III requires specific interactions to exist in nature (it is violated, for example, by sectors between which information cannot be copied); the distinguishability, consistency, and ensemble-distinguishability principles IV, V, VIII, and IX were conjectured with the authors' caveat that the paper's theorems need them to hold only for a special class of substrates, not universally; and the preparation and composition principles VI and VII assume unlimited generic resources, which the source concedes are violated in cosmological models with finite resources for computation. Establish, or refute, the consistency and universality of these principles over a precisely defined class of subsidiary theories, and determine whether the composition principle requires modification under finite resources. The violation of VI and VII already conceded for finite-resource cosmologies does not by itself discharge this sub-question: what is required is the scope of the principles over a delimited class of subsidiary theories together with the status of the composition principle under resource bounds.

(2) Characterization and uniqueness. Characterize the full class of superinformation media — information media with at least two information observables whose mutually disjoint attributes have a union that is not an information observable — admitted by the principles, together with the class of superinformation theories instantiating them, including the decision-supporting subclass identified in the constructor theory of probability (a superinformation theory is called 'decision-supporting' when it is rich enough to support a Deutsch-Wallace-style decision-theoretic derivation of probabilities from measurement outcomes; this subclass is currently known only through sufficient conditions). Determine whether quantum theory is the only physical realization of superinformation, or whether other, post-quantum theories can instantiate it.

These two parts are jointly directed at one objective: establishing which theories of physics the constructor theory of information's conjectured laws actually permit, and where quantum theory sits among them. Both parts are mandatory and their sub-questions are not independently sufficient: part (1) requires both the scope of principles III-IX over the delimited class of subsidiary theories and the resource-bounded status of VI-VII, and part (2) requires both the characterization of the superinformation-media class and the uniqueness question. Settling only one sub-question — in particular the uniqueness of quantum theory alone — is a partial result, not a completion of the task. The original open-question record also bundled the emergence of probability and the experimental testing of the principles; both have been substantially developed by later work and are treated here as progress context rather than as part of this completion boundary.

References

  1. David Deutsch and Chiara Marletto, 'Constructor theory of information', Proceedings of the Royal Society A 471 (2015) 20140540, DOI 10.1098/rspa.2014.0540, https://doi.org/10.1098/rspa.2014.0540 (preprint: arXiv:1405.5563, https://arxiv.org/abs/1405.5563).
  2. David Deutsch, 'Constructor theory', Synthese 190 (2013) 4331-4359, DOI 10.1007/s11229-013-0279-z, https://doi.org/10.1007/s11229-013-0279-z (the source paper's reference for the composition principle and the constructor-theory framework).
  3. Chiara Marletto, 'Constructor theory of probability', Proceedings of the Royal Society A 472 (2016) 20150883, DOI 10.1098/rspa.2015.0883, https://doi.org/10.1098/rspa.2015.0883 (preprint: arXiv:1507.03287, https://arxiv.org/abs/1507.03287).
  4. Chiara Marletto and Vlatko Vedral, 'Gravitationally Induced Entanglement between Two Massive Particles is Sufficient Evidence of Quantum Effects in Gravity', Physical Review Letters 119 (2017) 240402, DOI 10.1103/physrevlett.119.240402, https://doi.org/10.1103/PhysRevLett.119.240402.
  5. Chiara Marletto and Vlatko Vedral, 'Witnessing nonclassicality beyond quantum theory', Physical Review D 102 (2020) 086012, DOI 10.1103/physrevd.102.086012, https://doi.org/10.1103/PhysRevD.102.086012 (preprint: arXiv:2003.07974, https://arxiv.org/abs/2003.07974).
  6. Andrea Di Biagio, 'Gravity-induced entanglement is not a theory-independent witness of nonclassicality of the gravitational field', Physical Review D (accepted 1 September 2026), DOI 10.1103/r8ry-sp35, https://doi.org/10.1103/r8ry-sp35 (preprint: arXiv:2511.02683, https://arxiv.org/abs/2511.02683).
  7. Stefano Gogioso, Vincent Wang-Maścianica, Muhammad Hamza Waseem, Carlo Maria Scandolo, and Bob Coecke, 'Constructor Theory as Process Theory', Electronic Proceedings in Theoretical Computer Science 397 (2023), DOI 10.4204/eptcs.397.9, https://doi.org/10.4204/eptcs.397.9 (preprint: arXiv:2401.05364, https://arxiv.org/abs/2401.05364).
  8. David Deutsch and Chiara Marletto, 'Constructor theory of time', arXiv:2505.08692 (2025), https://arxiv.org/abs/2505.08692.
  9. Maria Violaris, 'Counterfactuals in Macroscopic Quantum Physics: Irreversibility, Measurement and Locality', PhD thesis, arXiv:2505.22834 (2025), https://arxiv.org/abs/2505.22834.
  10. Chiara Marletto, 'Constructor Theory of Thermodynamics', arXiv:1608.02625 (2016), https://arxiv.org/abs/1608.02625.
  11. Eduarda Fonseca da Nova Cruz and David Möckli, 'Quantum theories with local information flow', Brazilian Journal of Physics 54 (2024) 16, DOI 10.1007/s13538-023-01386-7, https://doi.org/10.1007/s13538-023-01386-7 (preprint: arXiv:2211.13325, https://arxiv.org/abs/2211.13325).