Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2103.13771 · Electronic Proceedings in Theoretical Computer Science

The Sheaf-Theoretic Structure of Definite Causality

Stefano Gogioso, Nicola Pinzani

Published Sep 9, 2021• 7 citations
arXivHTMLPDF

Abstract

We fill a gap in the study of contextuality by extending the sheaf-theoretic framework for non-locality by Abramsky and Brandenburger to deal with operational scenarios in the presence of arbitrary definite causal orders.
DOI
10.4204/eptcs.343.13

Related papers

The Contextuality-by-Default View of the Sheaf-Theoretic Approach to Contextuality

Ehtibar N. Dzhafarov

arXiv:1906.02718•Outstanding contributions to logic•Jan 1, 2023•10 citations

The Topology of Causality

Stefano Gogioso, Nicola Pinzani

We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality by Abramsky and Brandenburger, which it extends to include arbitrary causal orders (be they definite, dynamical or indefinite). We define a notion of causal function for arbitrary spaces of input histories, and we show that the explicit imposition of causal constraints on joint outputs is equivalent to the free assignment of local outputs to the tip events of input histories. We prove factorisation results for causal functions over parallel, sequential, and conditional sequential compositions of the underlying spaces. We prove that causality is equivalent to continuity with respect to the lowerset topology on the underlying spaces, and we show that partial causal functions defined on open sub-spaces can be bundled into a presheaf. In a striking departure from the Abramsky-Brandenburger setting, however, we show that causal functions fail, under certain circumstances, to form a sheaf. We define empirical models as compatible families in the presheaf of probability distributions on causal functions, for arbitrary open covers of the underlying space of input histories. We show the existence of causally-induced contextuality, a phenomenon arising when the causal constraints themselves become context-dependent, and we prove a no-go result for non-locality on total orders, both static and dynamical.

arXiv:2303.07148•Mar 13, 2023•1 citation

Detecting Contextuality: Sheaf Cohomology and All vs Nothing Arguments

Giovanni Carù

•Jan 1, 2015•5 citations

Stochastic Relational Presheaves and Dynamic Logic for Contextuality

Kohei Kishida

Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in quantum systems. After reviewing what presheaf models represent and what certain operations on them mean in terms of notions such as internal and external choices, composition of systems, and so on, I will show how to extend those models and ideas by combining them with ideas from other category-theoretic approaches to relational models and to stochastic processes. It turns out that my extension yields a transitional formulation of sheaf-theoretic structures that Abramsky and Brandenburger proposed to characterize non-locality and contextuality. An alternative characterization of contextuality will then be given in terms of a dynamic modal logic of the models I put forward.

arXiv:1412.8542•Electronic Proceedings in Theoretical Computer Science•Dec 27, 2014•3 citations

The Mathematical Structure of Non−locality locality & Contextuality

Shane Mansfield

•Jan 1, 2013•0 citations

Almost Equivalent Paradigms of Contextuality

Linde Wester

Various frameworks that generalise the notion of contextuality in theories of physics have been proposed; one is the sheaf-theoretic approach by Abramsky and Brandenburger; an other is the equivalence-based approach by Spekkens. We show that these frameworks are equivalent for scenarios with preparations and measurements, whenever factorizability is justified. This connection gives rise to a categorical isomorphism between suitable categories. We combine the advantages of the two approaches to derive a canonical method for detecting contextuality in such settings.

arXiv:1708.00843•Electronic Proceedings in Theoretical Computer Science•Feb 27, 2018•7 citations
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality by Abramsky and Brandenburger, which it extends to include arbitrary causal orders (be they definite, dynamical or indefinite). We define a notion of causal function for arbitrary spaces of input histories, and we show that the explicit imposition of causal constraints on joint outputs is equivalent to the free assignment of local outputs to the tip events of input histories. We prove factorisation results for causal functions over parallel, sequential, and conditional sequential compositions of the underlying spaces. We prove that causality is equivalent to continuity with respect to the lowerset topology on the underlying spaces, and we show that partial causal functions defined on open sub-spaces can be bundled into a presheaf. In a striking departure from the Abramsky-Brandenburger setting, however, we show that causal functions fail, under certain circumstances, to form a sheaf. We define empirical models as compatible families in the presheaf of probability distributions on causal functions, for arbitrary open covers of the underlying space of input histories. We show the existence of causally-induced contextuality, a phenomenon arising when the causal constraints themselves become context-dependent, and we prove a no-go result for non-locality on total orders, both static and dynamical.
Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in quantum systems. After reviewing what presheaf models represent and what certain operations on them mean in terms of notions such as internal and external choices, composition of systems, and so on, I will show how to extend those models and ideas by combining them with ideas from other category-theoretic approaches to relational models and to stochastic processes. It turns out that my extension yields a transitional formulation of sheaf-theoretic structures that Abramsky and Brandenburger proposed to characterize non-locality and contextuality. An alternative characterization of contextuality will then be given in terms of a dynamic modal logic of the models I put forward.
Various frameworks that generalise the notion of contextuality in theories of physics have been proposed; one is the sheaf-theoretic approach by Abramsky and Brandenburger; an other is the equivalence-based approach by Spekkens. We show that these frameworks are equivalent for scenarios with preparations and measurements, whenever factorizability is justified. This connection gives rise to a categorical isomorphism between suitable categories. We combine the advantages of the two approaches to derive a canonical method for detecting contextuality in such settings.