The Sheaf-Theoretic Structure of Definite Causality
arXiv:2103.13771 · doi:10.4204/EPTCS.343.13
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.
arXiv commentThis paper has been superseded by arXiv:2206.08911v4, arXiv:2303.07148 and arXiv:2303.09017. Specifically, Definition 3 of Locale of Inputs given in this work is not fit for purpose: Spaces of Input Histories, cf. Definition 3.8 of arXiv:2206.08911v4, should be used instead. If you wish to cite our work or built upon it, this is unlikely to be the right reference
References in corpus (38)
- Quantum correlations with no causal order
- Informational derivation of Quantum Theory
- Quantum computations without definite causal structure
- Probabilistic theories with purification
- The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
- Experimental Verification of an Indefinite Causal Order
- Beyond Bell's Theorem: Correlation Scenarios
- Indefinite Causal Order in a Quantum Switch
- Theory-independent limits on correlations from generalised Bayesian networks
- The contextual fraction as a measure of contextuality
- Quantum correlations in the temporal CHSH scenario
- Logical Bell Inequalities
- The simplest causal inequalities and their violation
- Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
- The Cohomology of Non-Locality and Contextuality
- Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios
- Cyclic Quantum Causal Models
- Quantum Advantage from Sequential-Transformation Contextuality
- Contextuality, Cohomology and Paradox
- Causality re-established
- Categorical Probabilistic Theories
- Terminality implies non-signalling
- Perfect signaling among three parties violating predefined causal order
- Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality
- On the Cohomology of Contextuality
- A comonadic view of simulation and quantum resources
- The Quantum Monad on Relational Structures
- Non-locality, contextuality and valuation algebras: a general theory of disagreement
- Consequences and applications of the completeness of Hardy's nonlocality
- Time-asymmetry of probabilities versus relativistic causal structure: an arrow of time
- Possibilities Determine the Combinatorial Structure of Probability Polytopes
- Categories of Empirical Models
- Contextuality and noncommutative geometry in quantum mechanics
- Logic of Local Inference for Contextuality in Quantum Physics and Beyond
- The logic of contextuality
- Cohomology and the Algebraic Structure of Contextuality in Measurement Based Quantum Computation
- Almost Equivalent Paradigms of Contextuality
- Stochastic Relational Presheaves and Dynamic Logic for Contextuality