By Carlos González-Guillén (Universidad Politécnica de Madrid)
Abstract: 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.
