  We study the generation of hybrid entanglement in a one-dimensional quantum
walk. In particular, we explore the preparation of maximally entangled states
between position and spin degrees of freedom. We address it as an optimization
problem, where the cost function is the Schmidt norm. We then benchmark the
algorithm and compare the generation of entanglement between the Hadamard
quantum walk, the random quantum walk and the optimal quantum walk. Finally, we
discuss an experimental scheme with a photonic quantum walk in the orbital
angular momentum of light. The experimental measurement of entanglement can be
achieved with quantum state tomography.
