Quasi-inversion of Quantum and Classical Channels in Finite Dimensions

The question

A noisy channel can lose information, so simply applying its mathematical inverse may not be a physically valid operation. What is the best recovery channel when exact reversal is unavailable?

The work

This paper develops the concept of a quasi-inverse for finite-dimensional quantum and classical channels. It establishes general properties and finds quasi-inverses for broad classes of channels.

For quantum channels, the recovery is assessed through the average fidelity between a random pure input state and the state obtained after the original channel and its quasi-inverse. The framework extends earlier qubit results to arbitrary finite dimensions and to classical channels.