The maximal coin-walker entanglement in quantum walks with ballistic transports

We experimentally show the first realization of the maximal entanglement under a ballistic quantum transport. An inhomogeneous ordered quantum walk is introduced to generate the maximal entanglement meanwhile maintaining the quadratic speedup, wherein the coin operations keep unchanged with time evolution but are varied according to positions in a deterministic way. Using a reconfigurable time-bin encoded optical network, we implement a 11-step ballistic quantum walk and obtain a maximal entanglement in which the von Neumann entropy of the coin state is close to 1. The construction of the maximal entanglement and the speedup of spreading signify a quadratic acceleration in producing entanglement with fast expansion of the Hilbert space, thus may stimulate the engineering of entanglement and the design of quantum algorithms.