Superdense coding with time-frequency Gottesman-Kitaev-Preskill states

We proposed a new superdense coding protocol using entangled time-frequency Gottesman-Kitaev-Preskill (TFGKP) states, standard telecommunication fiber components, time-resolving single-photon detectors, and frequency beam-splitter (FBS), demonstrating the possibility of superdense coding with currently achievable technologies. This scheme encodes information into conjugate time and frequency domains and requires an FBS for decoding. For practical experimental parameters, our scheme achieves a total transmission capacity of 8.86 bits per transmitted photon, equivalent to 465 distinguishable messages when considering asymptotically vanishing errors. Our TFGKP state-based superdense coding approach exceeds the rate achieved by frequency modulation in a single-photon frequency comb with the same parameters by more than 440 times and the rate achieved by temporal modulation by 4.7 times. Our approach has strong error resilience and operational simplicity using mostly passive devices. Consequently, this is a practical solution, particularly suitable for combining high-rate superdense coding, with quantum communication tasks involving multidimensional TFGKP states.