Generalized platypus channels have private and classical capacity 1 and show super-additive quantum capacity when combined with erasure or multilevel amplitude-damping channels.
Watrous, The Theory of Quantum Information(Cam- bridge University Press, 2018)
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Super-additivity of quantum capacity in simple channels
Generalized platypus channels have private and classical capacity 1 and show super-additive quantum capacity when combined with erasure or multilevel amplitude-damping channels.