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arXiv · 1311.7571

On the convergence of output sets of quantum channels

Benoit Collins·Motohisa Fukuda·Ion Nechita
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Abstract

We study the asymptotic behavior of the output states of sequences of quantum channels. Under a natural assumption, we show that the output set converges to a compact convex set, clarifying and substantially generalizing results in [BCN13]. Random mixed unitary channels satisfy the assumption; we give a formula for the asymptotic maximum output infinity norm and we show that the minimum output entropy and the Holevo capacity have a simple relation for the complementary channels. We also give non-trivial examples of sequences $Φ_n$ such that along with any other quantum channel $Ξ$, we have convergence of the output set of $Φ_n$ and $Φ_n\otimes Ξ$ simultaneously; the case when $Ξ$ is entanglement breaking is investigated in details.

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Benoit Collins, Motohisa Fukuda, Ion Nechita. 2013-11-29. On the convergence of output sets of quantum channels. https://doi.org/10.7900/jot.2013dec04.2008

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