Quasi-inversion of quantum and classical channels in finite dimensions

TL;DR

This paper introduces the concept of quasi-inverses for quantum and classical channels in finite dimensions, extending previous results and showing how they can improve fidelity in quantum state transformations.

Contribution

It defines and analyzes quasi-inverses for channels in arbitrary finite dimensions, expanding the scope of previous work and including classical channels.

Findings

Quasi-inverses can increase average fidelity of quantum states.

General properties of quasi-inverses are established.

Explicit determination of quasi-inverses for many channels.

Abstract

We introduce the concept of quasi-inverse of quantum and classical channels, prove general properties of these inverses and determine them for a large class of channels acting in an arbitrary finite dimension. Therefore we extend the previous results of [1] to arbitrary dimensional channels and to the classical domain. We demonstrate how application of the proposed scheme can increase on the average the fidelity between a given random pure state and its image transformed by the quantum channel followed by its quasi-inversion.