2014/05/31 by Bob Coecke
Physics and Astronomy · Computer Science · Mathematics · #quant-ph #cs.LO #math.CT
paper · pdf · doi:10.4204/eptcs.172.3
published as EPTCS 172, 2014, pp. 27-35 · In Proceedings QPL 2014, arXiv:1412.8102
arxiv created 2014/12/30 · arxiv updated 2014/12/31
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.