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原文摘要

Cellular communication is done over an imperfectly predictable multimode environment, where the sender only knows about the distribution of possible intermode coupling and scattering a signal faces. It may thus seem surprising that such communication is efficient. Telatar proved that the sender's lack of exact knowledge about the channel, on average, does not significantly hinder multimode communication. As the number $N$ of modes increases at fixed signal-to-noise ratio, the average capacity of a classical multimode fading channel grows linearly in $N$, like that of $N$ decoupled single-mode channels. We study the quantum analogue in a Haar-random passive bosonic network and prove a similar scaling for unassisted quantum information transmission. Suppose that the sender drives a fixed fraction of the input modes and the receiver collects more than half of the output modes. Then the quantum capacity of such channels at zero temperature grows linearly with the number of modes at fixed photon number per mode, just like the classical capacity grows with the number of antennas. At nonzero temperature, the Haar-averaged coherent information of the isotropic thermal input bounds the capacity from below, and its value per mode converges to an integral against Wachter's law. We numerically identify positive achievable rates in models motivated by cryogenic microwave networks and room-temperature multimode fibers.