Local model of a qudit: Single particle in optical circuits

It has been said about quantum interference, that "in reality, it contains the only mystery". Together with nonlocality, it is often considered the characteristic feature of quantum theory challenging our classical understanding of the world. In this work, we are concerned with the restricted setting of a single particle propagating in multipath interferometric circuits—that is, the physical realization of a qudit—which is host to many typically quantum mechanical effects including collapse of the wave function and contextuality. In this paper, we show that this framework can be simulated with classical resources without violating the locality principle. We present a local ontological model whose predictions are indistinguishable from the quantum case. In the model, `nonlocality' appears merely as an epistemic effect arising from a level of description by agents whose knowledge is incomplete. It is notably different from the multiparticle scenarios where entanglement leads to nonlocal correlations on an ontological level. This result exposes the conceptual difference between single- and multiparticle phenomena, pointing to the latter as a deeper quantum mystery.