Embedding cyclic information-theoretic structures in acyclic space-times: No-go results for indefinite causality

Alongside its companion in $P\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}y\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l$ $R\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}w$ $L\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s$, this paper reports on the similarities and differences between the information-theoretic and relativistic notions of causality, bringing them together under a single framework. This sheds light on a long-standing debate on whether experimentally realizable processes are truly indefinite causal ordered processes.