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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. This two-state coin-operator approach overcomes the intricacies caused by the utilization of high-dimensional coin operators required in prior studies of discrete-time quantum walks on fractals. In fulfilling the blank space on the analysis of the impact of inhomogeneity in quantum walk properties, specifically, fractal deterministic inhomogeneity, our results show a robust effect of entanglement enhancement as well as an interesting road to superdiffusive spreading with a tunable scaling exponent attaining robust superdiffusion, subballistic though. Explicitly, with this fractal approach it is possible to obtain an increase in quantum entanglement with reduced impact on standard quantum walk theoretical spreading. Alongside those features, we analyze further properties such as the degree of interference and visibility. The present model corresponds to an application of fractals in an experimentally viable setting, namely, the building block for the construction of photonic patterned structures. Published by the American Physical Society 2024
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