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We propose a protocol to simulate the evolution of a non-Markovian openquantum system by considering a collisional process with a many-body system,which plays the role of an environment. As a result of our protocol theenvironment spatial correlations are mapped into the time correlations of anoise that drives the dynamics of the open system. Considering the weakcoupling limit the open system can also be considered as a probe of theenvironment properties. In this regard, when preparing the environment in itsground state, a measurement of the dynamics of the open system allows todetermine the length of the environment spatial correlations and therefore itscritical properties. To illustrate our proposal we simulate the full systemdynamics with matrix-product-states and compare this with the reduced dynamicsobtained with an approximated variational master equation.

Quantum Critical Probing and Simulation of Colored Quantum Noise