Here are some of the quantum & geometric aspects of information processing studied

Quantum channels and their capacities;
Quantum cryptography;
Quantum control and error correction;
Entanglement characterization;
Quantum hypothesis testing and quantum estimation;

Information geometry;
Relativistic quantum information processes in curved spacetimes;
Cosmological entanglement;
Information and black holes;
p-adic and adelic formulation of quantum information processes;