  The Choi-state is an indispensable tool in the study and analysis of quantum
channels. Considering a channel in terms of its associated Choi-state can
greatly simplify problems. It also offers an alternative approach to the
characterisation of a channel, with properties of the Choi-state providing
novel insight into a channel's behaviour. The rank of a Choi-state, termed the
Choi-rank, has proven to be an important characterising property, and here, its
significance is further elucidated through an operational interpretation. The
Choi-rank is shown to provide a universal bound on how successfully two agents,
Alice and Bob, can perform an entanglement-assisted exclusion task. The task
can be considered an extension of super-dense coding, where Bob can only output
information about Alice's encoded bit-string with certainty. Conclusive state
exclusion, in place of state discrimination, is therefore considered at the
culmination of the super-dense coding protocol. In order to prove this result,
a necessary condition for conclusive k-state exclusion of a set of states is
presented in order to achieve this result, and the notions of weak and strong
exclusion are introduced.
