Characterization of a damping channel as a mixture of amplitude damping and anti-damping channels of different parameters

Open quantum systems frequently interact with their environments, leading to non-unital noise such as amplitude damping that exchanges energy and translates states on the Bloch sphere. While standard models like the generalized amplitude damping channel link decay parameters and mixing probabilities tightly through fixed system-environment interactions, this paper investigates a broader class of phase-covariant dynamics. The authors construct these dynamics by taking a convex mixture of amplitude-damping and anti-damping channels characterized by unequal decay parameters and independently controllable, time-dependent mixing probabilities. This approach bypasses the limitations of conventional thermal models to engineer specific open-system behaviors.

To analyze the resulting quantum channels, the authors employ a general theorem for positivity divisibility and demonstrate how evaluating it in suitably chosen Hilbert space bases simplifies the derivation of tractable constraints. They map out a comprehensive hierarchy of quantum Markovianity and non-Markovianity, ordering classes from the most restrictive dynamical semigroups down through completely positive divisible and positive divisible maps, to broader distance-based Breuer-Laine-Piilo Markovianity. By relating the master equation Lindblad rates directly to the dynamical map parameters, the study clarifies how different choices of rates and derivative behaviors govern transitions between unital and non-unital regimes.

By physically constructing the dynamics via the convex mixing of elementary completely positive processes, the framework guarantees complete positivity without requiring full prior knowledge of the microscopic system-environment Hamiltonian. The authors show that this independent tuning of contraction and translation terms yields an effective dephasing contribution absent in standard generalized amplitude damping models. Furthermore, they demonstrate that appropriate channel mixing can successfully reduce state deviation from an ideal noiseless evolution, and that this improvement can persist even after tuning the dynamics into a unital regime.