On the convergence of output sets of quantum channels

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 ${\Phi }_n$ such that along with any other quantum channel $\Xi$, we have convergence of the output set of ${\Phi }_n$ and ${\Phi }_n\otimes \Xi$ simultaneously; the case when $\Xi$ is entanglement breaking is investigated in details.

References in corpus (3)

• Moments and Cumulants of Polynomial random variables on unitary groups, the Itzykson-Zuber integral and free probability
• Asymptotics of random density matrices
• Remarks on the classical capacity of quantum channel

Cited by in corpus (6)

• Random matrix techniques in quantum information theory
• Random positive operator valued measures
• Additivity rates and PPT property for random quantum channels
• On the minimum output entropy of random orthogonal quantum channels
• Moment Methods on compact groups: Weingarten calculus and its applications
• Additivity violation of quantum channels via strong convergence to semi-circular and circular elements