  We introduce a probabilistic version of the one-shot quantum dense coding
protocol in both two- and multiport scenarios, and refer to it as conclusive
quantum dense coding. Specifically, we analyze the corresponding capacities of
two-qubit, two-qutrit, and three-qubit shared states. We identify cases where
Pauli and generalized Pauli operators are not sufficient as encoders to attain
the optimal one-shot conclusive quantum dense coding capacities. We find that
there is a rich connection between the capacities, and the bipartite and
multipartite entanglements of the shared state.
