Eternal non-Markovianity of qubit maps

TL;DR

This paper investigates the conditions under which qubit maps exhibit eternal non-Markovianity, revealing that non-unital maps cannot sustain eternal non-Markovianity, unlike certain unital maps which can be formed by specific convex combinations.

Contribution

It demonstrates that non-unital qubit maps cannot have eternal non-Markovianity, contrasting with unital maps that can be constructed from convex combinations of dephasing semigroups.

Findings

Non-unital maps cannot exhibit eternal non-Markovianity.

Unital maps can be eternally non-Markovian if formed by specific convex combinations.

Not all convex combinations of dephasing semigroups lead to eternal non-Markovianity.

Abstract

As is well known, unital Pauli maps can be eternally non-CP-divisible. In contrast, here we show that in the case of non-unital maps, eternal non-Markovianity in the non-unital part is ruled out. In the unital case, the eternal non-Markovianity can be obtained by a convex combination of two dephasing semigroups, but not all three of them. We study these results and ramifications arising from them.