We show that the new quantum extension of Renyi's \alpha-relative entropies,
introduced recently by Muller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J.
Math. Phys. 54, 122203, (2013), and Wilde, Winter, Yang, Commun. Math. Phys.
331, (2014), have an operational interpretation in the strong converse problem
of quantum hypothesis testing. Together with related results for the direct
part of quantum hypothesis testing, known as the quantum Hoeffding bound, our
result suggests that the operationally relevant definition of the quantum Renyi
relative entropies depends on the parameter \alpha: for \alpha<1, the right
choice seems to be the traditional definition, whereas for \alpha>1 the right
choice is the newly introduced version.
As a sideresult, we show that the new Renyi \alpha-relative entropies are
asymptotically attainable by measurements for \alpha>1, and give a new simple
proof for their monotonicity under completely positive trace-preserving maps.Comment: v5: Added Appendix A on monotonicity and attainability propertie
