Abstract
The eternally non-Markovian Pauli channel is an example of a unital channel characterized by a negative decay rate for all time t>0. Here we consider the problem of constructing an analogous non-unital channel, and show in particular that a d-dimensional generalized amplitude damping (GAD) channel cannot be eternally non-Markovian when the non-Markovianity originates solely from the non-unital part of the channel. We study specific ramifications of this result for qubit GAD. Specifically, we construct a quasi-eternally non-Markovian qubit GAD channel, characterized by a time t^∗ > 0, such that the channel is non-Markovian only and for all time t > t^∗. We further point out that our negative result for the qudit GAD channel, namely the impossibility of the eternal non-Markovian property, does not hold for a general qubit or higher-dimensional non-unital channel.