Quasi-inversion of quantum and classical channels in finite dimensions

Abstract We introduce the concept of quasi-inverse quantum and classical channels, prove general properties these inverses determine them for a large class channels acting in an arbitrary finite dimension. Therefore we extend previous results Karimipour et al (2020 Phys. Rev. A 101 032109) to dimensional domain. demonstrate how application proposed scheme can increase on average fidelity between given random pure state its image transformed by channel followed quasi-inversion.