Superclassical non-Markovian open quantum dynamics

We characterize a class of superclassical non-Markovian open quantum system dynamics that are defined by their lack of measurement invasiveness when the corresponding observable commutates with the pre-measurement state. This diagonal non-invasiveness guarantees that joint probabilities for measurement outcomes fulfill classical Kolmogorov consistency conditions. These features are fulfilled regardless of the previous (measurement) system history and are valid at arbitrary later times after an arbitrary system initialization. It is shown that a subclass of depolarizing dynamics, which are based on a (time-irreversible) non-unitary system-environment coupling, satisfy the required properties. The relationship with other operational [Milz et al., Phys. Rev. X 10, 041049 (2020)] and non-operational [Banacki et al., Phys. Rev. A 107, 032202 (2023)] notions of classicality in non-Markovian open quantum systems is studied in detail and exemplified through different examples.