Counterexamples to additivity of minimum output p-Renyi entropies of channels, for parameter p>2, p>1 and p near 0

The 'standard' additivity conjectures are about entropic quantities associated to channels: Holevo capacity and minimum output entropy. While these are still open, there is a long-standing approach using Renyi entropies. For a long time they have been conjectured to obey similar additivity relations, but this has recently been disproved. The talk is based on the author's preprint arXiv:0707.0402, and Patrick Hayden's more recent arXiv:0707.3291, plus as yet unpublished work by Chris King, and further counterexamples at p=0 due to the author with Toby Cubitt, Aram Harrow, Debbie Leung and Ashley Montanaro.