Probabilistic superdense coding
Arun Kumar Pati, Preeti Parashar, Pankaj Agrawal · Physical Review A · 2005
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 $2\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}d$ 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 $2\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}d$ classical bits with a shared resource of a higher dimensional entangled state $(D\ifmmode\times\else\texttimes\fi{}D,D>d)$. It is found that more entanglement does not necessarily lead to higher success probability. This also answers the question as to why we need ${\mathrm{log}}_{2}d$ ebits to send $2\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}d$ classical bits in a deterministic fashion.