  We are at the midst of second quantum revolution where the mesoscopic quantum
devies are actively employed for technological purposes. Despite this fact, the
description of their real-time dynamics beyond the Fermi's golden rule remains
a formiddable theoretical problem. This is due to the rapid spread of
entanglement within the degrees of freedom of the surrounding environment. This
is accompanied with a quantum noise (QN) acting on the mesoscopic device. In
this work we propose a possible way out: to exploit the fact that this QN is
usually bandlimited. This is because its spectral density is often contained in
peaks of localized modes and resonances, and may be constrained by bandgaps.
Inspired by the Kotelnikov sampling theorem from the theory of classical
bandlimited signals, we put forward and explore the idea that when the QN
spectral density has effective bandwidth $B$, the quantum noise becomes a
discrete-time process, with an elementary time step $\tau\propto B^{-1}$. After
each time step $\tau$, one new QN degree of freedom (DoF) gets coupled to the
device for the first time, and one new QN DoF get irreversibly decoupled. Only
a bounded number of QN DoFs are significantly coupled at any time moment. We
call these DoFs the \textit{Kotelnikov modes}. As a result, the real-time
dissipative quantum motion has a natural structure of a discrete-time matrix
product state, with a bounded bond dimension. This yields a microscopically
derived collision model. The temporal entanglement entropy appears to be
bounded (area-law scaling) in the frame of Kotelnikov modes. The irreversibly
decoupled modes can be traced out as soon as they occur during the real-time
evolution. This leads to a novel\textit{bandlimited} input-output formalism and
to quantum jump Monte Carlo simulation techniques for real-time motion of open
quantum systems. We illustrate this idea on a spin-boson model.
