01373nas a2200169   4500000000100000000000100001008004100002100001600043700002200059700001900081700002200100245004800122856003800170300001100208490000700219520097700226       2018                            d1 aIon Nechita1 aZbigniew Puchała1 aŁukasz Pawela1 aKarol Życzkowski00aAlmost all quantum channels are equidistant  uhttps://doi.org/10.1063/1.5019322  a0522010 v593 a<p>In this work we analyze properties of generic quantum channels in the case of large system size. We use the random matrix theory and free probability to show that the distance between two independent random channels tends to a constant value as the dimension of the system grows larger. As a measure of the distance we use the diamond norm. In the case of a flat Hilbert-Schmidt distribution on quantum channels, we obtain that the distance converges to <span style="font-size:129%">1/2<em>+2/π</em></span>. Furthermore, we show that for a random state <span style="font-size:129%"><em>ρ</em></span> acting on a bipartite Hilbert space $H_A \otimes H_B$, sampled from the Hilbert-Schmidt distribution, the reduced states $Tr_A\rho$ and $Tr_B \rho$ are arbitrarily close to the maximally mixed state. This implies that, for large dimensions, the state <span style="font-size:129%"><em>ρ</em></span> may be interpreted as a Jamio{\l}kowski state of a unital map.</p>