Terminality implies non-signalling

Bob Coecke

doi:10.4204/eptcs.172.3

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arXiv · 1405.3681

Terminality implies non-signalling

Bob Coecke

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Abstract

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 sense of non-signalling in process theories. We conclude that because of its much simpler mathematical form, terminality should be taken to be a more fundamental notion than non-signalling.

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Bob Coecke. 2014-05-14. Terminality implies non-signalling. https://doi.org/10.4204/eptcs.172.3

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