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In this work we analyze properties of generic quantum channels in the case oflarge system size. We use random matrix theory and free probability to showthat the distance between two independent random channels converges to aconstant value as the dimension of the system grows larger. As a measure of thedistance we use the diamond norm. In the case of a flat Hilbert-Schmidtdistribution on quantum channels, we obtain that the distance converges to$\frac12 + \frac{2}{\pi}$, giving also an estimate for the maximum successprobability for distinguishing the channels. We also consider the problem ofdistinguishing two random unitary rotations.

Almost all quantum channels are equidistant