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This is achieved using a passive linear photonic reservoir in which a photodiode at the optical-to-electrical interface provides the sole source of nonlinearity. We demonstrate how the requirements of different tasks can be quantified and compared to the dynamics provided by the reservoir by explicitly calculating and comparing the contributing monomials. Our findings show that a reservoir with uncoupled virtual nodes and a quadratic nonlinearity can already achieve good performance for tasks derived from dynamical systems with quadratic nonlinearities, such as the Lorenz63 system. 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