Master equation for cascade quantum channels: a collisional approach

It has been recently shown that collisional models can be used to derive a general form for the master equations which describe the reduced time evolution of a composite multipartite quantum system, whose components 'propagate' in an environmental medium which induces correlations among them via a cascade mechanism. Here, we analyse the fundamental assumptions of this approach showing how some of them can be lifted when passing into a proper interaction picture representation.