# Almost all quantum channels are equidistant

 Title Almost all quantum channels are equidistant Publication Type Journal Article Year of Publication 2018 Authors Nechita I, Puchała Z, Pawela Ł, Życzkowski K Journal Journal of Mathematical Physics Volume 59 Pagination 052201 Abstract 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 1/2+2/π. Furthermore, we show that for a random state ρ 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 ρ may be interpreted as a Jamio{\l}kowski state of a unital map. URL https://doi.org/10.1063/1.5019322 DOI 10.1063/1.5019322 Reprint Edition arXiv:1612.00401