Simplifying additivity problems using direct sum constructions

@article{Fukuda2007SimplifyingAP,
title={Simplifying additivity problems using direct sum constructions},
author={M. Fukuda and M. Wolf},
journal={Journal of Mathematical Physics},
year={2007},
volume={48},
pages={072101}
}

We study the additivity problems for the classical capacity of quantum channels, the minimal output entropy, and its convex closure. We show for each of them that additivity for arbitrary pairs of channels holds if and only if it holds for arbitrary equal pairs, which in turn can be taken to be unital. In a similar sense, weak additivity is shown to imply strong additivity for any convex entanglement monotone. The implications are obtained by considering direct sums of channels (or states) for… Expand