When describing or observing a physical phenomenon, it is generally assumed that there exists an underlying causal order to the events. The belief is that events which occur later in time can be influenced by events occurring at earlier times, but not the other way around. Recently, however there has been an intensified interest in the role that quantum mechanics has to play when describing causal order in physical phenomena. Principles fundamental and unique to quantum mechanics can be exploited in such a way that they appear to result in descriptions of processes with indefinite causal structures. 

In this talk we look at two formalisms. The first is that of multi-time states, first introduced by Aharanov and colleagues, who developed a time-symmetric formulation of quantum theory. Here, a quantum system at several different times is described by associating a quantum state to each time.  The second work we look at is the process matrix formalism, introduced by Oreshkov, Costa, and Brukner. Here, the idea of the 'process matrix' was introduced as a possible generalisation of quantum states where the causal structure of events can be partially relaxed. Here, operations in local laboratories are described by quantum theory without assuming a global causal structure.

At first glance, the two approaches appear to be completely different and unrelated. We show that every process matrix is shown to correspond to a two-time state (the converse link however does not hold in general). We also provide an extension of a result which characterises process matrices. The connection presented here allows us to apply new methods and concepts to the issue of physics with indefinite causal structure, open new questions and hopefully create a platform of discussion about the issues of time and causality in quantum theory.