Superdense Coding Using Higher Dimensional Embedding

Quantum dense coding is a foundational protocol in quantum communication, allowing two classical bits to be transmitted by sending a single qubit when a maximally entangled pair is shared. In this work, we consider Embedded Dense Coding (EDC)-a generalization of deterministic dense coding that embeds one subsystem into a higher-dimensional Hilbert space. To assess the operational advantage of EDC compared to standard dense coding, we consider the probability of transmission error when fixing the rate of entanglement consumed per classical message sent. We first demonstrate that EDC enables a smaller one-shot transmission error compared to standard dense coding when using quantum channels with nonzero rates of dephasing and loss. We then demonstrate that even with noiseless communication channels, EDC leads to smaller overall errors when the sender and receiver have noisy local processors. This advantage is shown through concrete implementations of EDC on IBM's Heron processor.