论星际量子通信与费米悖论
On Interstellar Quantum Communication and the Fermi Paradox
AI总结：
本文首次分析星际量子信道容量，给出实现非零容量所需的波长与望远镜直径阈值，并据此提出费米悖论的新解释。
摘要：
自其发端以来\cite{CocconiMorrison}，搜寻地外智慧生命（SETI）一直聚焦于星际经典通信。最近，Berera\cite{Berera:2020rpl}指出，在某些频率下，光子量子比特能够在星际（甚至星系际）距离上保持其量子相干性，从而带来了星际量子通信的前景。这是一种引人入胜的可能性，因为量子通信允许完成某些经典通信不可能实现的任务，并能为其他任务带来指数级加速。（我们在星际语境下提出了若干动机。）但仅有量子相干性并不足以实现量子通信：在这里，我们首次分析星际信道的量子容量$Q$。我们指出，要拥有非零量子容量$Q>0$，距离为$L$的星际通信必须使用波长$λ<26.5\\,cm$（以避免宇宙微波背景导致的退极化），并使用有效直径$D>0.78\sqrt{λL}$的巨型望远镜（以满足量子擦除约束）。例如，对于地球和Proxima Centauri上两台直径为$D$的望远镜，这意味着$D>100\\,km$！这是可靠单向量子通信成为可能之前仍需跨越的技术门槛，并提示了费米悖论的一种根本性新解答。
英文摘要：
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 $λ< 26.5\,cm$ (to avoid depolarization by the cosmic microwave background), and \emph{enormous} telescopes of effective diameter $D>0.78\sqrt{λL}$ (to satisfy quantum erasure constraints). For example, for two telescopes of diameter $D$ on Earth and Proxima Centauri, this implies $D>100\,km$! 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.
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