Probabilistic superdense coding

Abstract

We explore the possibility of performing superdense coding with nonmaximally entangled states as a resource. Using this we find that one can send two classical bits in a probabilistic manner by sending a qubit. We generalize our scheme to higher dimensions and show that one can communicate 2 log₂d classical bits by sending a d-dimensional quantum state with a certain probability of success. The success probability in superdense coding is related to the success probability of distinguishing nonorthogonal states. The optimal average success probabilities are explicitly calculated. We consider the possibility of sending 2 log₂d classical bits with a shared resource of a higher dimensional entangled state (D × D, D > d). It is found that more entanglement does not necessarily lead to higher success probability. This also answers the question as to why we need log₂d ebits to send 2 log₂d classical bits in a deterministic fashion.