Channel-capacity gain in entanglement-assisted communication protocols based exclusively on linear optics, single-photon inputs, and coincidence photon counting

Abstract

Entanglement can effectively increase communication channel capacity as evidenced by dense coding that predicts a capacity gain of $1\phantom{\rule{4.pt}{0ex}}\text{bit}$ when compared to entanglement-free protocols. However, dense coding relies on Bell states and when implemented using photons the capacity gain is bounded by $0.585\phantom{\rule{4.pt}{0ex}}\text{bits}$ 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 $0.585\phantom{\rule{4.pt}{0ex}}\text{bits}$? 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 $N=6,8$.