Recently Szangolies has argued (in the setting of extended Wigner's-friend scenarios) that quantum theory permits ``Rashomon'' situations: multiple internally coherent accounts of events that cannot be combined into a single, consistent global narrative. This note explains why the Rashomon phenomenon can be understood as a \emph{failure of gluing}: local descriptions over different contexts exist, but they do not admit a single global ``all-perspectives-at-once'' description. This is the same mathematical obstruction that underlies modern sheaf-theoretic treatments of contextuality. I then indicate why the same perspective is useful in parts of the social sciences (quantum-like modelling of cognition, judgment, and decision-making), where ``context effects'' can likewise be interpreted as the absence of a single joint probability space.
Recently Szangolies has argued (in the setting of extended Wigner's-friend scenarios) that quantum theory permits Rashomon'' situations: multiple internally coherent accounts of events that cannot be combined into a single, consistent global narrative. This note explains why the Rashomon phenomenon can be understood as a \emph{failure of gluing}: local descriptions over different contexts exist, but they do not admit a single global all-perspectives-at-once'' description. This is the same mathematical obstruction that underlies modern sheaf-theoretic treatments of contextuality. I then indicate why the same perspective is useful in parts of the social sciences (quantum-like modelling of cognition, judgment, and decision-making), where ``context effects'' can likewise be interpreted as the absence of a single joint probability space.
The Frauchiger-Renner argument aims to show that `quantum theory cannot consistently describe the use of itself': in many-party settings where agents are themselves subject to quantum experiments, agents may make predictions that contradict observations. Here, we introduce a simplified setting using only three agents, that is independent of the initial quantum state, thus eliminating in particular any need for entanglement, and furthermore does not need to invoke any final measurement and resulting collapse. Nevertheless, the predictions and observations made by the agents cannot be integrated into a single, consistent account. We propose that the existence of this sort of \emph{Rashomon effect}, i.e. the impossibility of uniting different perspectives, is due to failing to account for the limits put on the information available about any given system as encapsulated in the notion of an \emph{epistemic horizon}.
Abramsky and Brandenburger show that nonlocality and contextuality arise when locally compatible data cannot be glued into a single global assignment. In a global topological data space, interactions among locally defined maps can produce patterns that are consistent within each context yet incompatible globally—the empirical hallmark of quantum contextuality. We make this concrete with an evolving simplicial-bundle framework and apply this framework to several standard empirical models in quantum foundations.
In quantum physics, the term ‘contextual’ can be used in more than one way. One usage, here called ‘Bell contextual’ since the idea goes back to Bell, is that if A , B and C are three quantum observables, with A compatible (i.e. commuting) with B and also with C , whereas B and C are incompatible, a measurement of A might yield a different result (indicating that quantum mechanics is contextual) depending upon whether A is measured along with B (the { A , B } context) or with C (the { A , C } context). An analysis of what projective quantum measurements measure shows that quantum theory is Bell non-contextual: the outcome of a particular A measurement when A is measured along with B would have been exactly the same if A had, instead, been measured along with C . A different definition, here called ‘globally (non)contextual’ refers to whether or not there is (non-contextual) or is not (contextual) a single joint probability distribution that simultaneously assigns probabilities in a consistent manner to the outcomes of measurements of a certain collection of observables, not all of which are compatible. A simple example shows that such a joint probability distribution can exist even in a situation where the measurement probabilities cannot refer to properties of a quantum system, and hence lack physical significance, even though mathematically well defined. It is noted that the quantum sample space, a projective decomposition of the identity, required for interpreting measurements of incompatible properties in different runs of an experiment using different types of apparatus, has a tensor product structure, a fact sometimes overlooked. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.
A set of quantum data can look classical in every local test and still fail to admit a single classical explanation of the whole composite system. We formulate this failure as global contextuality. Here global means global in the physical sense of the whole multipartite system, not the local/global terminology of sheaf theory. Each party's local statistics are noncontextual and each measured multipartite context admits a generalized local hidden-variable description, but the GLHV block descriptions cannot be promoted to a single noncontextual hidden-variable model for the whole system. Three bipartite constructions exhibit this separation. A polarization-path construction gives a direct global obstruction. A qubit-qutrit KCBS construction gives an algebraic scenario-level example, with explicit formulas for the unconditional KCBS operator, the correlation-polytope constraints, and the postselected violation. A flagged qutrit Werner-local state gives a state-level example: the state is entangled and local for all projective measurements, its local qutrit marginals do not violate KCBS, yet postselection rules out a single GNCHV model. We also spell out the classical composition lemma: classical conditional hidden variables can be absorbed into a larger hidden variable, whereas quantum contextual data need not allow such a factorization. Within the general Bell-type framework considered here, with arbitrary parties and arbitrary local compatible contexts, but no cross-party joint measurements, the absence of local contextuality and GLHV-type generalized Bell nonlocality does not imply the existence of a global noncontextual hidden-variable model. Global contextuality is thus a compositional obstruction to classical explanation.
The main subjects of this thesis are non-locality and contextuality, two fundamental features of quantum mechanics that constitute valuable resources for quantum computation. Our analysis is based on Abramsky & Brandenburger's sheaf theoretic framework, which captures both these phenomena in a unified treatment and in a very general setting. This high-level description transcends quantum physics and allows to precisely characterise the notion of contextuality as the apparent paradox realised by data being locally consistent but globally inconsistent. More specifically, we aim to develop a deeper understanding of so-called logical forms of contextuality, i.e. situations where the phenomenon can be witnessed using purely logical arguments, disregarding probabilities. The sheaf theoretic description of logical contextuality has recently inspired the development of a topological treatment of the phenomenon based on sheaf cohomology. In this thesis, we embark on a detailed analysis of the cohomology of contextuality, exposing key shortcomings in the current methods, and introducing an (almost) complete cohomological characterisation of logical forms of contextuality. More specifically, we show that, in its current formulation, sheaf cohomology does not constitute a complete invariant for contextuality, not even in its strongest forms, and that higher cohomology groups cannot be used to study the phenomenon. Then, we solve these issues by introducing a novel construction, which derives refined versions of the presheaves describing empirical models to expose their deeper extendability properties, resulting in a sheaf cohomological invariant which is applicable to the vast majority of empirical models, and conjectured to work universally. We propose a general theory of contextual semantics using the language of valuation algebras. In particular, we give a general definition of contextual behaviour as a fundamental gap between local agreement and global disagreement of information sources. Not only does this formalism aptly capture and generalise the known instances of contextuality beyond quantum theory, but it also provides inspiration for further applications of the phenomenon, and paves the way for the transfer of results and techniques between different fields. We give a prime example of this potential by developing faster algorithms to detect contextuality based on mainstream methods of generic inference. Finally, we turn our attention back to instances of contextuality in quantum physics, and study strong contextuality in multi-qubit states. We give a complete combinatorial characterisation of All-vs-Nothing proofs of strong contextuality in stabiliser quantum mechanics. This allows to produce the complete list of all stabiliser states exhibiting this kind of contextuality, which consitututes an important resource in certain models of quantum computation. Then, we extend our search for strongly contextual behaviour beyond stabiliser states, and identify the minimum quantum resources needed to realise strong non-locality. Additional results include a partial classification of strongly non-local models comprised of three-qubit states and local projective measurements, and the introduction of a new infinite family of strongly non-local three-qubit states.