Generating Page-scrambled states and teleporting quantum information with engineered fast scramblers

Page-scrambled states are pure quantum states in which every subsystem, A, up to |A| < N/2 for an N-component system exhibits maximal entanglement entropy. We show that such states can be generated deterministically with O[log(N)] operations in a family of quantum circuits that can be implemented, e.g., using neutral atom arrays and Rydberg excitations. We discuss how these dynamics can be a resource to investigate many-body quantum teleportation following a protocol proposed by Yoshida and Yao in the context of a Hayden-Preskill experiment. We conclude that this family of circuits can outperform circuits with only local interactions, producing higher recovered fidelities especially in the presence of noise, and scrambles as efficiently as randomly coupled qubits.