2017/01/03 by Aleks Kissinger, Sander Uijlen
Computer Science · #cs.OH
paper · pdf · doi:10.4204/eptcs.236.6
published as EPTCS 236, 2017, pp. 87-94 · In Proceedings QPL 2016, arXiv:1701.00242
arxiv created 2017/01/03 · arxiv updated 2017/01/04
Following on from the notion of (first-order) causality, which generalises the notion of being tracepreserving from CP-maps to abstract processes, we give a characterization for the most general kind of map which sends causal processes to causal processes. These new, second-order causal processes enable us to treat the input processes as 'local laboratories' whose causal ordering needs not be fixed in advance. Using this characterization, we give a fully-diagrammatic proof of a non-trivial theorem: namely that being causality-preserving on separable processes implies being 'completely' causality preserving. That is, causality is preserved even when the 'local laboratories' are allowed to have ancilla systems. An immediate consequence is that preserving causality is separable processes is equivalence to preserving causality for strongly non-signalling (a.k.a. localizable) processes.