Reversibility of a quantum channel: general conditions and their applications to Bosonic linear channels

TL;DR

This paper establishes general conditions for the reversibility of quantum channels, especially Bosonic linear channels, providing explicit criteria, physical interpretations, and applications in quantum information theory.

Contribution

It introduces a comprehensive method using complementary channels to determine reversibility conditions for Bosonic linear channels, including explicit constructions and applications.

Findings

Reversibility conditions for Bosonic linear channels are derived.

Explicit construction of reversing channels confirms sufficiency.

Conditions for classical-quantum subchannels and depolarizing subchannels are established.

Abstract

The method of complementary channel for analysis of reversibility (sufficiency) of a quantum channel with respect to families of input states (pure states for the most part) are considered and applied to Bosonic linear (quasi-free) channels, in particular, to Bosonic Gaussian channels. The obtained reversibility conditions for Bosonic linear channels have clear physical interpretation and their sufficiency is also shown by explicit construction of reversing channels. The method of complementary channel gives possibility to prove necessity of these conditions and to describe all reversed families of pure states in the Schrodinger representation. Some applications in quantum information theory are considered. Conditions for existence of discrete classical-quantum subchannels and of completely depolarizing subchannels of a Bosonic linear channel are obtained in the Appendix.