We investigate, both numerically and experimentally, the usefulness of a distributed non-linearity in a passive coherent photonic reservoir computer. This computing system is based on a passive coherent optical fiber-ring cavity in which part of the non-linearities are realized by the Kerr non-linearity. Linear coherent reservoirs can solve difficult tasks but are aided by non-linear components in their input and/or output layer. Here, we compare the impact of non-linear transformations of information in the reservoirs input layer, its bulk—the fiber-ring cavity—and its readout layer. For the injection of data into the reservoir, we compare a linear input mapping to the non-linear transfer function of a Mach Zehnder modulator. For the reservoir bulk, we quantify the impact of the optical Kerr effect. For the readout layer we compare a linear output to a quadratic output implemented by a photodiode. We find that optical non-linearities in the reservoir itself, such as the optical Kerr non-linearity studied in the present work, enhance the task solving capability of the reservoir. This suggests that such non-linearities will play a key role in future coherent all-optical reservoir computers.