Quantum correlations in time

We investigate quantum correlations in time in different approaches, under the assumption that temporal correlations should be treated in an even-handed manner with spatial correlations. We compare the pseudo-density matrix formalism with several other approaches: indefinite causal structures, consistent histories, generalised quantum games, out-of-time-order correlations(OTOCs), and path integrals. We establish relationships among these space-time approaches in non-relativistic quantum theory, and show that they are closely related and map into each other. This results in a unified picture in which temporal correlations in different space-time approaches are the same or operationally equivalent. However, the path integral formalism defines correlations in terms of amplitude measure rather than probability measure in other approaches, thus do not fit into the unified picture.