Quantum walks with spatiotemporal fractal disorder

Abstract

We investigate the transport and entanglement properties exhibited by quantum walks with coin operators concatenated in a space-time fractal structure. Inspired by recent developments in photonics, we choose the paradigmatic Sierpinski gasket. The 0-1 pattern of the fractal is mapped into an alternation of the generalized Hadamard-Fourier operators. In fulfilling the blank space on the analysis of the impact of disorder in quantum walk properties -- specifically, fractal deterministic disorder --, our results show a robust effect of entanglement enhancement as well as an interesting novel road to superdiffusive spreading with a tunable scaling exponent attaining effective ballistic diffusion. Namely, with this fractal approach it is possible to obtain an increase in quantum entanglement without jeopardizing spreading. Alongside those features, we analyze further properties such as the degree of interference and visibility. The present model corresponds to a new application of fractals in an experimentally feasible setting, namely the building block for the construction of photonic patterned structures.