Abstract
A ‘process theory’ is any theory of systems and processes which admits sequential and parallel composition. ‘Terminality’ unifies normalisation for pure states, trace-preservation for positive superoperators, and adding up to identity of positive operators in quantum theory, and it moreover generalises this to arbitrary process theories. We show that terminality and no-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 no-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 no-signalling. We also point out that terminality imposes many other nice features upon process theories, for example, it even imposes relativistic covariance.
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Coecke, B. Terminality Implies No-signalling ...and Much More Than That. New Gener. Comput. 34, 69–85 (2016). https://doi.org/10.1007/s00354-016-0201-6
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DOI: https://doi.org/10.1007/s00354-016-0201-6