  Entanglement can effectively increase communication channel capacity as
evidenced by dense coding that predicts a capacity gain of 1 bit when compared
to entanglement-free protocols. However, dense coding relies on Bell states and
when implemented using photons the capacity gain is bounded by $0.585$ bits due
to one's inability to discriminate between the four optically encoded Bell
states. In this paper we study the following question: Are there alternative
entanglement-assisted protocols that rely only on linear optics, coincidence
photon counting and separable single photon input states and at the same time
provide a greater capacity gain than $0.585$ bits. We show that besides the
Bell states there is a class of bipartite four-mode two-photon entangled states
that facilitate an increase in channel capacity. We also discuss how the
proposed scheme can be generalized to the case of two-photon $N$-mode entangled
states for $N=6,8$.
