This question is about the difference between Quantum Mutual Information and Holevo Information of quantum channels. From http://arxiv.org/pdf/1004.2495.pdf equation 7 we know that the sum of quantum mutual informtions of a channel and that of its complementary channel is equal to two times the von Neumannn entropy of the input state. Can we say the same about the Holevo informations of a channel and its complementary channel?:
So from what I understand the Holevo information is equal to the mutual information when mutual information is maximized over the channel's input:
If this is true what is the resulting corrlation between the Holevo informations of the channel and that of the complementary channel?
Thank you for your input.