Reversibility conditions for quantum channels and their applications

TL;DR

This paper establishes conditions under which quantum channels are reversible for certain state families and provides a comprehensive classification of such channels, with implications for quantum information theory.

Contribution

It offers a necessary condition for reversibility of quantum channels and fully characterizes channels reversible with respect to specific state families, connecting to operator algebra theory.

Findings

Derived a necessary condition for reversibility with bounded rank families

Provided a complete classification of reversible channels for pure state families

Connected reversibility conditions to operator algebra theory

Abstract

A necessary condition for reversibility (sufficiency) of a quantum channel with respect to complete families of states with bounded rank is obtained. A full description (up to isometrical equivalence) of all quantum channels reversible with respect to orthogonal and nonorthogonal complete families of pure states is given. Some applications in quantum information theory are considered. The main results can be formulated in terms of the operator algebras theory (as conditions for reversibility of channels between algebras of all bounded operators).