On the eternal non-Markovianity of non-unital quantum channels

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 $t^{\ast }>0$, such that the channel is non-Markovian only and for all time $t>t^{\ast }$. 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.

13 pages, 2 figures; Accepted in International Journal of Quantum Information

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