Geometric Rényi Divergence and its Applications in Quantum Channel Capacities

We present a systematic study of the geometric R\'enyi divergence (GRD), also known as maximal divergence, from point view quantum information theory. show that this together with its extension to channels, has many appealing structural properties. For example we prove chain rule inequality immediately implies "amortization collapse" for addressing an open question by Berta et al. [arXiv:1808.01498, Equation (55)] in area channel discrimination. As applications, explore various capacity problems and construct new measures based on sharpening previously best-known bounds max-relative entropy while still keeping single-letter efficiently computable. A plethora examples are investigated improvements evident almost all cases.