Convexity of reverse coherent information capacity and its application

Reverse coherent information, as a symmetric counterpart of the coherent information, has been firstly defined by R. García-Patrón et al. This quantity allows to define reverse coherent information capacity which is additive. In this Letter, we prove the convexity of such capacity for a general quantum channel, and investigate the effect of convex decomposition of quantum channel on its (reverse) coherent information. Finally, we apply the convexity property to provide an upper bound on the reverse coherent information capacity for some important channels.

► It is proved that reverse coherent information capacity is convex.
► Reverse coherent information is more sensitive to convex decomposition than counterpart.
► Upper bounds on reverse coherent information capacity for some channels are provided.