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.

16 pages, 9 figures

References in corpus (8)

• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Dynamics of continuous-time quantum walks in restricted geometries
• Transport properties of continuous-time quantum walks on Sierpinski fractals
• $1/f^{\alpha }$ spectra in elementary cellular automata and fractal signals
• Maximal coin-position entanglement generation in a quantum walk for the third step and beyond regardless of the initial state
• Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states
• Simulation of the multiphase configuration and phase transitions with quantum walks utilizing a step-dependent coin
• Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator