Maximal coin-walker entanglement in a ballistic quantum walk

We report the position-inhomogeneous quantum walk (IQW) can be utilized to produce the maximal high dimensional entanglement while maintaining the quadratic speedup spread of the wave-function. Our calculations show that the maximal coin-walker entanglement can be generated in any odd steps or asymptotically in even steps, and the nearly maximal entanglement can be obtained in even steps after $2$. We implement the IQW by a stable resource-saving time-bin optical network, in which a polarization Sagnac loop is employed to realize the precisely tunable phase shift. Our approach opens up an efficient way for high-dimensional entanglement engineering as well as promotes investigations on the role of coin-walker interactions in QW based applications.