A short well-written starting point is Carlton Caves' on-line notes "Completely positive maps, positive maps, and the Lindblad form", see in particular Caves' discussion following (eq. 21), and the references provided.

It helps also to have a physical appreciation of "unravelling" as applied to quantum operations (the alternate spelling "unraveling" is common too); this term was (AFAICT) first introduced in Howard Carmichael's *An Open Systems Approach to Quantum Optics* (1993, see Section 7.4, p. 122).

In summary, a clear appreciation of the physical process of unravelling quantum trajectories, and the mathematical description of quantum trajectory unravelling as a Markov processes of Lindblad form, will go far to answer your questions.

No doubt other folks can recommend favorite references; please do so.

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