Werner gap in presence of simple coloured noise

A `Werner gap' is the range of relevant parameters characterising a quantum state for which it is both entangled and admits local hidden variable model. Werner showed that the gap becomes maximal for entanglement mixed with white noise if subsystems have infinitely many levels. Here we study pure entangled states mixed with simple coloured noise modelled as a single pure product state. We provide an explicit local hidden variable model for quantum correlations of some states of this family and give hints that likely there is a model for all quantum predictions. This demonstrates essentially maximal Werner gap already for two qubits. Additionally to fundamental interest the study has implications for quantum computation and communication.