Appears in collection : Probabilistic techniques and Quantum Information Theory

We consider random quantum channels arising form uniform random isometries via the Stinespring representation. We will show that these channels are generically gapped, that is, there is a separation between the first and second singular values of the channels. We will see that, in a broad sense, this result can be seen as a generalisation of Hasting's result for a set of random unital channels. Moreover, we will discuss different applications of this result to study entropy and correlations in 1D tensor networks.