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Two new classes of quantum channels, which we call more capable and lessnoisy, are introduced. The more capable class consists of channels such thatthe quantum capacities of the complementary channels to the environments arezero. The less noisy class consists of channels such that the privatecapacities of the complementary channels to the environment are zero. For themore capable class, it is clarified that the private capacity and quantumcapacity coincide. For the less noisy class, it is clarified that the privatecapacity and quantum capacity can be single letter characterized.

Private and Quantum Capacities of More Capable and Less Noisy Quantum Channels