  Phase plays a crucial role in many quantum effects including interference.
Phase is normally defined in terms of complex numbers that appear when
representing quantum states as complex vectors. Here we give an operational
definition whereby phase is instead defined in terms of measurement statistics.
Our definition is phrased in terms of the operational framework known as
generalised probabilistic theories, or the convex framework. The definition
makes it possible to ask whether other theories in this framework can also have
phase. We apply our definition to investigate phase and interference in several
example theories: classical probability theory, a version of Spekken's toy
model, quantum theory, and box-world. We find that phase is ubiquitous; any
non-classical theory can be said to have non-trivial phase dynamics.
