PrerequisiteLinear algebra; Matrix analysisAbstractThis course will focus on a formal presentation of definitions and theorems on quantum channels in quantum information theory. Numerous mathematical proofs of these theorems will be showed
AbstractWe introduce an quantum entropy for bimodule quantum channels on finite von Neumann algebras, generalizing the remarkable Pimsner-Popa entropy. The relative entropy for Fourier multipliers of bimodule quantum channels establishes an upper bound of the quantum entropy. Additionally, we present the Araki relative entropy for bimodule quantum channels, revealing its equivalence to the rela...