Local model of a qubit in the interferometric setup

We consider a typical realization of a qubit as a single particle in two-path interferometric circuits built from phase shifters, beam splitters and detectors. This framework is often taken as a standard example illustrating various paradoxes and quantum effects, including non-locality. In this paper we show that it is possible to simulate the behaviour of such circuits in a classical manner using stochastic gates and two kinds of particles, real ones and ghosts, which interact only locally. The model has built-in limited information gain and state disturbance in measurements which are blind to ghosts. We demonstrate that predictions of the model are operationally indistinguishable from the quantum case of a qubit, and allegedly 'non-local' effects arise only on the epistemic level of description by the agent whose knowledge is incomplete due to the restricted means of investigating the system.