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We present novel and simple estimation of a minimal dimension required for aneffective reservoir in open quantum systems. Using a tensor network formalismwe introduce a new object called a reservoir network (RN). The reservoirnetwork is the tensor network in the form of a Matrix Product State, whichcontains all effects of open dynamics. This object is especially useful forunderstanding memory effects. We discuss possible applications of the reservoirnetwork and the estimation of dimension to develop new numerical and machinelearning based methods for open quantum systems.

Dimension truncation for open quantum systems in terms of tensor networks