Bosonic and Fermionic Discrete-Time Quantum Walk on Integrated Optics

In recent years, quantum walks have been proposed as widely applicable in virtually every science related discipline. In fact, they have emerged as a useful tool in the development of quantum algorithms and have been proposed as promising resources for the simulation of physical quantum systems. Single-particle quantum walks have been experimentally demonstrated by different approaches, while only few realizations of 2-particle quantum walks have been given so far. More in general, the realization of quantum walks of many of particles travelling in a more complex network is still an open question. Here we investigate the behaviour of two entangled photons traversing a 6-step discrete quantum walk built on an array of 36 integrated waveguide beam splitters. By exploiting polarization entanglement of the particles we were able to simulate the bunching-antibunching behaviour of non interacting bosons and fermions. We have also characterized the possible distinguishability and decoherence effects arising in such a structure. This study is necessary in view of the realization of a quantum simulator based on an integrated optical array built on a large number of beam splitters.