  In this paper, we study the power of sequential decoding strategies for
several channels with classical input and quantum output. In our sequential
decoding strategies, the receiver loops through all candidate messages trying
to project the received state onto a `typical' subspace for the candidate
message under consideration, stopping if the projection succeeds for a message,
which is then declared as the guess of the receiver for the sent message. We
show that even such a conceptually simple strategy can be used to achieve rates
up to the mutual information for a single sender single receiver channel called
cq-channel henceforth, as well as the standard inner bound for a two sender
single receiver multiple access channel, called ccq-MAC in this paper. Our
decoding scheme for the ccq-MAC uses a new kind of conditionally typical
projector which is constructed using a geometric result about how two subspaces
interact structurally.
  As the main application of our methods, we construct an encoding and decoding
scheme achieving the Chong-Motani-Garg inner bound for a two sender two
receiver interference channel with classical input and quantum output, called
ccqq-IC henceforth. This matches the best known inner bound for the
interference channel in the classical setting. Achieving the Chong-Motani-Garg
inner bound, which is known to be equivalent to the Han-Kobayashi inner bound,
answers an open question raised recently by Fawzi et al. (arxiv:1102.2624). Our
encoding scheme is the same as that of Chong-Motani-Garg, and our decoding
scheme is sequential.
