A collision model (CM) is a framework to describe open quantum dynamics. In its memoryless version, it models the reservoir $\mathcal{R}$ as consisting of a large collection of elementary ancillas: the dynamics of the open system $\mathcal{S}$ results from successive collisions of $\mathcal{S}$ with the ancillas of $\mathcal{R}$. Here, we present a general formulation of memoryless composite CMs, where $\mathcal{S}$ is partitioned into the very open system under study $S$ coupled to one or more auxiliary systems $\left\{S_i\right\}$. Their composite dynamics occurs through internal $S-\left\{S_i\right\}$ collisions interspersed with external ones involving $\left\{S_i\right\}$ and the reservoir $\mathcal{R}$. We show that important known instances of quantum non-Markovian dynamics of $S$—such as the emission of an atom into a reservoir featuring a Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random telegraph noise—can be mapped on to such memoryless composite CMs.

• Received 11 May 2017

DOI:https://doi.org/10.1103/PhysRevA.96.032107