Excitation-damping quantum channels

TL;DR

This paper introduces a class of quantum channels modeling population transfer between excited and ground states, generalizing amplitude-damping channels, and characterizes their mathematical properties and conditions for complete positivity.

Contribution

It provides necessary and sufficient conditions for the complete positivity of these channels and explores their behavior in time-dependent, Markovian scenarios.

Findings

Necessary and sufficient conditions for complete positivity.

Equivalence of complete positivity and simple positivity when ground sector is one-dimensional.

Characterization of CP-divisible channels and Markovian semigroups within this class.

Abstract

We study a class of quantum channels describing a quantum system, split into the direct sum of an excited and a ground sector, undergoing a one-way transfer of population from the former to the latter; this construction, which provides a generalization of the amplitude-damping qubit channel, can be regarded as a way to upgrade a trace non-increasing quantum operation, defined on the excited sector, to a possibly trace preserving operation on a larger Hilbert space. We provide necessary and sufficient conditions for the complete positivity of such channels, and we also show that complete positivity is equivalent to simple positivity whenever the ground sector is one-dimensional. Finally, we examine the time-dependent scenario and characterize all CP-divisible channels and Markovian semigroups belonging to this class.