Abstract: It is by now well known that both the minimal output entropy of a quantum
channel and its capacity for transmitting quantum information are non-additive.
However, explicit examples remain elusive.
Gour and Friedland showed that the minimal output entropy of a quantum channel
is locally additive. This result can be extended to the
maximal output relative entropy H(P,Q) = Tr P ( log P - log Q )
when the second argument Q is fixed. This can be used to obtain a necessary
and sufficient condition for superadditivity of the classical capacity of a quantum
channel which does not require finding either the capacity or the optimal input
average of the product channel.
I'll sketch the proof of local additivity and discuss the implications for a
numerical search for superadditivity.