Abstract
Since it began \cite{CocconiMorrison}, the search for extraterrestrial intelligence (SETI) has focused on interstellar \emph{classical} communication. Recently, Berera \cite{Berera:2020rpl} pointed out that, at certain frequencies, photon qubits can retain their quantum coherence over interstellar (and even intergalactic) distances, raising the prospect of interstellar \emph{quantum} communication. This is an intriguing possibility, since quantum communication permits certain tasks that would be impossible with classical communication, and allow exponential speed-ups for others. (We suggest some motivations in the interstellar context.) But quantum coherence alone is not sufficient for quantum communication: here, for the first time, we analyze the \emph{quantum capacity} Q of an interstellar channel. We point out that, to have non-zero quantum capacity Q>0, interstellar communication over a distance L must use wavelengths λ < 26.5cm (to avoid depolarization by the cosmic microwave background), and \emph{enormous} telescopes of effective diameter D>0.78√λ L (to satisfy quantum erasure constraints). For example, for two telescopes of diameter D on Earth and Proxima Centauri, this implies D>100km! This is a technological threshold that remains to be crossed in order for reliable one-way quantum communication to become possible, and suggests a fundamental new resolution of the Fermi paradox.