Phase boundaries in deterministic dense coding
Michael R. Beran, Scott M. Cohen · Physical Review A · 2009
We consider dense coding with partially entangled states on bipartite systems of dimension $d\ifmmode\times\else\texttimes\fi{}d$, studying the conditions under which a given number of messages, $N$, can be deterministically transmitted. It is known that the largest Schmidt coefficient, ${\ensuremath{\lambda}}_{0}$, must obey the bound ${\ensuremath{\lambda}}_{0}\ensuremath{\le}d/N$, and considerable empirical evidence points to the conclusion that there exist states satisfying ${\ensuremath{\lambda}}_{0}=d/N$ for every $d$ and $N$ except the special cases $N=d+1$ and $N={d}^{2}\ensuremath{-}1$. We provide additional conditions under which this bound cannot be reached---that is, when it must be that ${\ensuremath{\lambda}}_{0}