Resource theory of causal connection

The capacity of distant parties to send signals one another is a fundamental requirement in many information-processing tasks. Such ability determined by the causal structure connecting parties, and more generally, intermediate processes carrying from laboratory another. Here we build fully fledged resource theory connection for all multi-party communication scenarios, encompassing those where operate definite order also indefinite. We define characterize set free three different sets transformations thereof, resulting distinct theories connection. In causally ordered setting, identify most resourceful bipartite tripartite scenarios. general instead, our results suggest that there no global valuable resource. establish signalling robustness as monotone provide tight bounds on it pertinent processes. Finally, introduce non-separability, show -- contrast case unique. Together offer flexible comprehensive framework quantify transform quantum processes, well insights into their multi-layered structures.