In 1958 P.W. Anderson predicted that the wave-function of a quantum particle can be localized in the presence of a static disordered potential [1]. This phenomenon arises from the destructive interference of waves propagating in static disordered media. As a consequence, in these conditions, particle and energy transport through a disordered medium are expected to be strongly suppressed and an initially localized wave packet does not spread out with time. In this work we experimentally study the localization properties of a pair of non-interacting particles obeying bosonic/fermionic statistics by simulating a one-dimensional QW of a two-photon polarization-entangled state in a disordered medium. Quantum walk is the quantum counterpart of classical random walk: a walker jumping between different sites of a lattice with a given probability. In the quantum case the walker is a quantum system, whose quantum properties affect the transport. When multi-particle walkers travel within the QW their bosonic or fermionic nature strongly affects the transport. Here we implement different quantum statistics by exploiting of the polarization-entangled bi-photon input state. The QW circuit has been experimentally realized by femtosecond laser writing which provides a perfect phase stability [2]. In particular, we realized an 8-step quantum walk circuit composed by an array of polarization independent beam splitters arranged in a cascade configuration of Mach-Zehnder (MZ) interferometers (see Fig.1a).
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