Abstract: The entropy exchange for channels and states ininfinite-dimensional systems are defined and studied. It is shownthat, this entropy exchange depends only on the given channel andthe state. An explicit expression of the entropy exchange in termsof the state and the channel is proposed. The generalized Klein'sinequality, the subadditivity and the triangle inequality about theentropy for the infinite-dimensional systems are proved and then, applied tocompare theentropy exchange with the entropychange.
