# Terminality implies non-signalling

@inproceedings{Coecke2014TerminalityIN, title={Terminality implies non-signalling}, author={Bob Coecke}, booktitle={QPL}, year={2014} }

A 'process theory' is any theory of systems and processes which admits sequential and parallel composition. `Terminality' unifies normalisation of pure states, trace-preservation of CP-maps, and adding up to identity of positive operators in quantum theory, and generalises this to arbitrary process theories. We show that terminality and non-signalling coincide in any process theory, provided one makes causal structure explicit. In fact, making causal structure explicit is necessary to even make…

## 30 Citations

Categorical Quantum Mechanics I: Causal Quantum Processes

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We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions.
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Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two…

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This work proposes to take agents as the basic building blocks through which the authors test a physical theory, and recover operational notions of locality from signalling conditions, and introduces an operational model for the effective state spaces of individual agents, as well as the range of their actions.

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The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in…

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We show that the physical principle "the adjoint associates to each state a `test' for that state" fully characterises the Hermitian adjoint for pure quantum theory, therefore providing the adjoint…

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- PhysicsArXiv
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We demonstrate how the key notions of Tononi et al.'s Integrated Information Theory (IIT) can be studied within the simple graphical language of process theories, i.e. symmetric monoidal categories.…

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It is found that it is possible to talk about classical correlations, quantum correlations and other kinds of correlations on any directed acyclic graph, and this captures various extensions of Bell scenarios that have been considered in the literature.

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