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We study the reduced time-evolution of open quantum systems by combiningquantum-information and statistical field theory. Inspired by prior work [EPL102, 60001 (2013) and Phys. Rev. Lett. 111, 050402 (2013)] we establish theexplicit structure guaranteeing the complete positivity (CP) andtrace-preservation (TP) of the real-time evolution expansion in terms of themicroscopic system-environment coupling.  This reveals a fundamental two-stage structure of the coupling expansion:Whereas the first stage defines the dissipative timescales of the system--before having integrated out the environment completely-- the second stagesums up elementary physical processes described by CP superoperators. Thisallows us to establish the nontrivial relation between the (Nakajima-Zwanzig)memory-kernel superoperator for the density operator and novel memory-kerneloperators that generate the Kraus operators of an operator-sum. Importantly,this operational approach can be implemented in the existing Keldysh real-timetechnique and allows approximations for general time-nonlocal quantum masterequations to be systematically compared and developed while keeping the CP andTP structure explicit.  Our considerations build on the result that a Kraus operator for a physicalmeasurement process on the environment can be obtained by 'cutting' a group ofKeldysh real-time diagrams 'in half'. This naturally leads to Kraus operatorslifted to the system plus environment which have a diagrammatic expansion interms of time-nonlocal memory-kernel operators. These lifted Kraus operatorsobey coupled time-evolution equations which constitute an unraveling of theoriginal Schr\"odinger equation for system plus environment. Whereas bothequations lead to the same reduced dynamics, only the former explicitly encodesthe operator-sum structure of the coupling expansion.

Density-operator evolution: Complete positivity and the Keldysh real-time expansion