Almost all quantum channels are equidistant

TytułAlmost all quantum channels are equidistant
Publication TypeJournal Article
Rok publikacji2018
AutorzyNechita I, Puchała Z, Pawela Ł, Życzkowski K
JournalJournal of Mathematical Physics
Volume59
Pagination052201
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.

URLhttps://doi.org/10.1063/1.5019322
DOI10.1063/1.5019322
Reprint EditionarXiv:1612.00401

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