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The quantum regression formula for an open quantum system consists in aninfinite hierarchy of conditions for its multi-time correlation functions, thusrequiring full access to the total "system+environment" evolution, andproviding a stronger requirement than CP-divisibility. Here, we analyzeCP-divisibility and check the validity of quantum regression beyond theBorn-Markov approximation (e.g. weak coupling limit) for a class of generalizedspin-boson (GSB) models giving rise to a multi-level amplitude-dampingevolution; in all cases, it is possible to engineer the system-bath coupling insuch a way that quantum regression is exactly satisfied.

Quantum regression beyond the Born-Markov approximation for generalized spin-boson models