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

Channel Capacity Gain in Entanglement-Assisted Communication Protocols Based Exclusevly on Linear Optics and Single Photon Inputs