Interference as an information-theoretic game

The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate higher-order interference theories. In this work we show that these pertain to broader class of processes, which can be formulated as information-processing tasks, providing cut classical, tasks involve two parties communication them with the goal winning certain parity games. We order is in one-to-one correspondence Furthermore, prove additive under composition systems both theory. latter result used (semi)device-independent witness number particles setting. Finally, extend our game formulation within generalized probabilistic framework tomographic locality implies additivity composition. These results shed light on operational meaning important for identification information-theoretic principles behind second-order