Stochastic versus Periodic Quantum Collision Models

Most literature on quantum collision models (CMs) usually considers periodic weak collisions featuring a fixed waiting time between two next collisions. Some works have yet addressed CMs with random waiting time and strong collisions (stochastic CMs). This short paper discusses how the open dynamics arising from these two types of models can be formally mapped with one another. This can be achieved for a given stochastic CM by constructing an associated periodic CM such that the waiting time randomness of the former is turned into the mixedness of the ancilla's initial state of the latter, introducing at the same time an additional state of the ancilla. Through this mapping, non-Markovian behaviour arising from a constrained number of stochatic collisions can be linked to initial ancilla-ancilla correlations of the associated periodic CM.

Automated summary

This paper discusses the formal mapping between the open dynamics of periodic weak collisions and stochastic strong collisions in quantum collision models. The author constructs an associated periodic model to represent the non-Markovian behavior of the stochastic model and introduces an ancilla state to represent the correlations between the two.