Optimal Encoding Capacity of a Linear Optical Quantum Channel

Here, we study the classical information capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. We present a 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., Knill-Laflamme-Milburn 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 (two photons in four modes). In this case, our protocol encodes one additional bit of information. Greater gains are expected for larger systems.