Geometric R\'{e}nyi Divergence and its Applications in Quantum Channel Capacities

Understand

We present a systematic study of the geometric R\'enyi divergence (GRD), also known as the maximal R\'enyi divergence, from the point of view of quantum information theory.

• We show that this divergence, together with its extension to channels, has many appealing structural properties.
• For example we prove a chain rule inequality that immediately implies the "amortization collapse" for the geometric R\'enyi divergence, addressing an open question by Berta et al.
• [arXiv:1808.01498, Equation (55)] in the area of quantum channel discrimination.