Abstract: In this talk I will discuss three distinct properties of the quantum, private and classical capacities of quantum channels which makes computing them very challenging: non-convexity, non-additivity and superactivation. I will discuss the techniques and ideas that are used to establish these properties for the quantum and private capacities and present a proof that private capacity is non-convex. My talk will be loosely based on two papers and one unpublished manuscript: D. Elkouss, S. Strelchuk “On the non-convexity of the private capacity” (unpublished) D. Elkouss, S. Strelchuk "Superadditivity of Private Information for Any Number of Uses of the Channel” Phys. Rev. Lett. 115, 040501 (2015) F. Brandao, J. Oppenheim, S. Strelchuk "When Does Noise Increase the Quantum Capacity?” Phys. Rev. Lett. 108, 040501 (2012)

Date: 06 January 2016