Maximal entanglement between a quantum walker and her quantum coin for the third step and beyond regardless of the initial state

Xiao-Xu Fang, Kui An, Bai-Tao Zhang, Barry C. Sanders, He Lu

Published 2022-09-05Version 1

We study maximal entanglement generation between a walker and her coin via a discrete-time quantum walk, in which the coin operation is randomly selected from one of two coin operators set at each step. We solve maximal-entanglement generation as an optimization problem with quantum process fidelity as the cost function. Then we determine an appropriate pair of one-parameter coins along with coin sequences that generate maximal entanglement, which is available for any step beyond the second regardless of initial condition. We further simplify the coin set to comprising Hadamard and identity operations, which are feasible experimentally. Experimentally, we demonstrate a ten-step quantum walk with such coin sequences and thereby show the desired high-dimensional bipartite entanglement.