Rigidity of superdense coding

The famous superdense coding protocol of Bennett and Wiesner demonstrates that it is possible to communicate two bits classical information by sending only one qubit using a shared EPR pair. Our first result an arbitrary for achieving this task (where there are no assumptions on the sender’s encoding operations or dimension entangled state) locally equivalent canonical Bennett-Wiesner protocol. In other words, rigid . particular, we show sender receiver use additional entanglement (beyond pair) as source randomness. We also investigate several questions about higher-dimensional coding, where goal d 2 messages -dimensional quantum state, general dimensions Unlike = case (i.e. single qubit), can be inequivalent protocols higher present concrete constructions protocols, based orthogonal unitary bases all > 2. Finally, analyze performance operators independently sampled from Haar measure group. analysis involves bounding distinguishability random maximally states, which may independent interest.