  Here, we study the capacity of a quantum channel, assuming linear optical
encoding, as a function of available photons and optical modes. First, we
observe that substantial improvement is made possible by not restricting
ourselves to a rail-encoded qubit basis. Then, we derive an analytic formula
for general channel capacity and show that this capacity is achieved without
requiring the use of entangling operations typically required for scalable
universal quantum computation, e.g. KLM measurement-assisted transformations.
As an example, we provide an explicit encoding scheme using the resources
required of standard dense coding using two dual-rail qubits (2 photons in 4
modes). In this case, our protocol encodes one additional bit of information.
Greater gains are expected for larger systems.
