Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We consider classical ontological models constrained to reuse a single ontic state space across multiple interventions. We prove an information-theoretic no-go theorem showing that such models must incur an irreducible contextual information cost: contextual dependence cannot be fully mediated through the ontic state alone and requires additional contextual information beyond it. We provide a constructive example illustrating this obstruction and show that it arises solely from the requirement of ontic state reuse within a classical probability space. We further explain how quantum theory avoids this obstruction by relaxing the assumption that all measurement statistics arise from a single underlying classical ontic variable. These results identify contextuality as a fundamental information-theoretic constraint on classical ontological models and clarify its origin as a limitation on classical representations.
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Version 2: Major revision. Reformulated fully within the ontological models framework and quantum contextuality in quantum foundations, following the approaches of Kochen-Specker, Spekkens, and Cabello. This work addresses foundational aspects of quantum theory and is intended for submission to PRX Quantum. Please consider adding quant-ph as a secondary category if appropriate
Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We consider classical ontological models constrained to reuse a single ontic state space across multiple interventions. We prove an information-theoretic no-go theorem showing that such models must incur an irreducible contextual information cost: contextual dependence cannot be fully mediated through the ontic state alone and requires additional contextual information beyond it. We provide a constructive example illustrating this obstruction and show that it arises solely from the requirement of ontic state reuse within a classical probability space. We further explain how quantum theory avoids this obstruction by relaxing the assumption that all measurement statistics arise from a single underlying classical ontic variable. These results identify contextuality as a fundamental information-theoretic constraint on classical ontological models and clarify its origin as a limitation on classical representations.
Contextuality is a central feature distinguishing quantum from classical probability theories, but its operational meaning is often stated only qualitatively. In this Letter, we study a simple information-theoretic question: how much additional contextual information must a classical simulation introduce when it tries to keep a shared internal description fixed across contexts? To make this question precise, we analyze a minimal external-label simulation model in which the remaining context dependence is carried only by an auxiliary label. For this model, we define an obstruction cost as the minimum mutual information between the context and the auxiliary label required to reproduce the observed statistics. We then prove a conservative quantitative lower bound: any linear witness that separates the observed statistics from the zero-obstruction set yields a positive lower bound on this cost. We do not claim that this bound is tight, and we do not claim that the simulation model covers every possible classical architecture. Its role is narrower and more explicit: under fixed shared-state semantics, contextuality can be read as a certificate of irreducible external bookkeeping cost in a simple and well-defined simulation model.
AI and collective intelligence systems universally suffer from a deficiency of context. There are innumerable possible contexts that may possibly change the interpretation of some signal, that may change the proper response to some stimulus. For example, an image understanding system that does not recognize an arrest event in a zoomed image of a person's face. How is it possible to know there is more information, outside of what the system can access, that affects the interpretation of data The solution to the context problem in practice today is a pragmatic, engineering one: analyze errors (in recommendations, question answers, image recognition, etc.), classify the kinds of contextual information that caused the wrong behavior, find the most common type of context that causes errors, and add information about that kind of context to the system. Clearly this approach is neither general nor scalable, and ignores the infamous long tail of possible contextual information that may affect a system's understanding and its behavior. In this paper we outline a new, more general, approach to recognizing context. The approach is grounded in a fairly simple intuition: the mathematics underlying quantum mechanics is far more appropriate for modeling, and therefore simulating, human cognitive behavior than the standard toolset from classical statistics. Notions such as Heisenberg's uncertainty principle, superpositions of states, and entanglement have direct and measurable analogs in collective intelligence.
The Informational Observer proposes a unified informational framework in which perception, measurement, and experienced reality emerge from the compression and reconstruction processes performed by observers. Instead of treating reality as an external, fixed entity, the model defines reality as the intersection of informational invariants preserved across multiple independent observers. Each biological, artificial, or simulated observer applies a compression operator to the underlying informational field and reconstructs an internal model shaped by priors, limitations, and energetic constraints.This framework explains perceptual variability across species, hallucinations in artificial and biological systems, observer-dependent measurement, and stability of physical laws. The model integrates cognitive science, AI interpretability, quantum contextuality, and simulation theory into a single informational principle, expanding the author’s Informational State Dynamics (ISD) framework. It introduces a general mechanism capable of unifying cross-domain phenomena through informational transformations. This work introduces The Informational Observer, a theoretical framework describing perception, measurement, and reality as the result of informational transformations performed by observing systems. The observer is conceptualized not as a passive receiver of sensory input, but as a compression system that selectively reduces the informational field into internal representations and reconstructs coherent experiential states. The model formalizes this process through two operators: Cᵢ (Compression): reduction of the informational field Ψᵢ (Reconstruction): predictive reconstruction of the compressed state Reality is defined as the set of informational invariants found in the intersection of reconstructions produced by different observers: Reality = ⋂ Ψᵢ(Cᵢ(I₀)) This perspective unifies phenomena that traditionally belong to different scientific domains: perceptual variability (human, animal, artificial systems) hallucinations and confabulation sensory filtering and cognitive priors observer-dependent physics and measurement nested or simulated universes informational emergence of the “self” The Informational Observer extends the author’s Informational State Dynamics (ISD) model and provides a foundation for future research in AI interpretability, cognitive modeling, neuroscientific theory, and information-based physics.
The context-sensitivity of cognition has been demonstrated across a wide range of cognitive functions such as perception, memory, judgement and decision making. A related term, 'contextuality', has appeared from the field of quantum cognition, with mounting empirical evidence demonstrating that cognitive phenomena are sometimes contextual. Contextuality is a subtle notion that influences how we must view the properties of the cognitive phenomenon being studied. This article addresses the questions: What does it mean for a cognitive phenomenon to be contextual? What are the implications of contextuality for probabilistic models of cognition? How does contextuality differ from context-sensitivity? Starting from George Boole's "conditions of possible experience", we argue that a probabilistic model of a cognitive phenomenon is necessarily subject to an assumption of realism. By this we mean that the phenomenon being studied is assumed to have cognitive properties with a definite value independent of observation. In contrast, quantum cognition holds that a cognitive property maybe indeterminate, i.e., its properties do not have well established values prior to observation. We argue that indeterminacy is sufficient for incompatibility between cognitive properties. In turn, incompatibility is necessary for their contextuality. The significance of this argument for cognitive psychology is the following:if a cognitive phenomenon is found to be contextual, then there is reason to believe it may be indeterminate. We illustrate by means of two crowdsourced experiments how context-sensitivity and contextuality of cognitive properties in the form of facial trait judgements can be characterized from empirical data. Finally, we conceptually and formally contrast contextuality with context-sensitivity. We propose that both involve a form of context dependence, with causality being the differentiating factor: the context dependence in context-sensitivity has a causal basis, whereas the context dependence in contextuality is acausal. The resulting implications for probabilistic models of cognition are discussed.
We propose an information -- theoretic framework for quantifying Kochen-Specker contextuality. Two complementary measures are introduced: the mutual information energy, a state-independent quantity inspired by Onicescu's information energy that captures the geometric overlap between joint eigenspaces within a context; and an operational measure based on commutator expectation values that reflects contextual behavior at the level of measurement outcomes. We establish a hierarchy of bounds connecting these measures to the Robertson uncertainty relation, including spectral, purity-corrected, and operator norm estimates. The framework is applied to the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) scenario for spin-1 systems, where all quantities admit closed-form expressions. The Majorana-stellar representation furnishes a common geometric platform on which both the operational measure and the uncertainty products can be analyzed. For spin-1, this representation yields a three-dimensional Euclidean-like visualization of the Hilbert space in which, states lying on a plane exhibit maximum uncertainty for the observable along the perpendicular direction; simultaneous optimization across all KCBS contexts singles out a unique state on the symmetry axis. Notably, states achieving the optimal sum of uncertainty products exhibit vanishing operational contextuality, while states with substantial operational contextuality satisfy a nontrivial Robertson bound -- the two extremes are achieved by distinct quantum states.
Recent theories developing broad notions of context and its effects on inference are becoming increasingly important in fields as diverse as cognitive psychology, information science and quantum information theory and computing. Here we introduce a novel and general approach to the characterisation of contextuality using the techniques of Chu spaces and Channel Theory viewed as general theories of information flow. This involves introducing three essential components into the formulism: events, conditions and measurement systems. Incorporating these factors in relationship to conditional probabilities leads to information flows both in the setting of Chu spaces and Channel Theory. The latter provides a representation of semantic content using local logics from which conditionals can be derived. We employ these features to construct cone-cocone diagrams, commutativity of which enforces inferential coherence. With these we build a scale-free architecture incorporating a Bayesian-like hierarchical structure, in which there is an interpretation of active inference and Markov blankets. We compare this architecture with other theories of contextuality which we briefly review. We also show that this development of ideas conveniently accommodates negative probabilities, leading to the notion of signed information flow, and address how quantum contextuality can be interpreted within this model. Finally, we relate contextuality to the Frame Problem, another way of characterising a fundamental limitation on the observational and inferential capabilities of finite agents.