title: Superadditivity of Private Information for Any Number of Uses of the Channel.
abstract: The quantum capacity of a quantum channel is always smaller than the capacity of the channel for private communication. Both quantities are given by the infinite regularization of the coherent and the private information, respectively, which makes their evaluation very difficult. Here, we construct a family of channels for which the private and coherent information can remain strictly superadditive for unbounded number of uses, thus demonstrating that the regularization is necessary. We prove this by showing that the coherent information is strictly larger than the private information of a smaller number of uses of the channel. This implies that even though the quantum capacity is upper bounded by the private capacity, the nonregularized quantities can be interleaved.
authors.affiliation: Departamento de Análisis Matemático and Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain.|QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands.
authors.forename: David
authors.initials: D
authors.lastname: Elkouss
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
authors.forename: Sergii
authors.initials: S
authors.lastname: Strelchuk