Recurrent generation of maximally entangled single particle states via quantum walks on cyclic graphs

Maximally entangled single particle states (MESPS) are opening new possibilities in quantum technologies as they have the potential to encode more information and are robust to decoherence compared to their non-local two-particle counterparts. Herein, using discrete-time quantum walks on $k$-cycles where $k\in\{3,4,5,8\}$ and by using either a single coin or effective-single coin or two coins in various deterministic sequences, we generate MESPS for recurring time steps. These sequences beget ordered quantum walks and yield MESPS with periods 4, 6, 9, 12, and 15. For the first time, we reveal single coins such as Hadamard, which can generate periodic MESPS (with periods 4 and 12) on $4$ and $8$-cycles. This scheme is resource-saving with possibly the most straightforward experimental realization since the same coin is applied at each time step.