Exploring the limits of no backward in time signalling

We present an operational and model-independent framework to investigate the concept of no-backwards-in-time signalling. We define no-backwards-in-time signalling conditions, closely related to spatial no-signalling conditions. These allow for theoretical possibilities in which the future affects the past, nevertheless without signalling backwards in time. This is analogous to non-local but non-signalling spatial correlations. Furthermore, our results shed new light on situations with indefinite causal structure, and their connection to quantum theory.