Quantum walks with quantum chaotic coins: Loschmidt echo, classical limit, and thermalization

Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo-like fidelity plays central role, and when the coin chaotic this approximately characteristic function of random walker. Thus binomial distribution arises walk walker exhibits diffusive growth before eventually becoming ballistic. The coin-walker entanglement be logarithmic in time case many-body localization coupled kicked rotors, saturates value depends on relative space dimensions. In coin-dominated scenario, chaos thermalize typical states such at Haar averaged Page value, unlike walker-dominated atypical seem produced.