The entanglement of deterministic aperiodic quantum walks

We study the entanglement between the internal(coin)and the external(position)degrees of freedom in the dynamic and the static deterministic aperiodic quantum walks(QWs).For the dynamic(static)aperiodic QWs,the coin depends on the time(position)and takes two coins C(α)and C(β)arranged in the two classes of generalized Fibonacci(GF)and the Thue–Morse(TM)sequences.We found that for the dynamic QWs,the entanglement of three kinds of the aperiodic QWs are close to the maximal value,which are all much larger than that of the homogeneous QWs.Further,the first class of GF(1st GF)QWs can achieve the maximum entangled state,which is similar to that of the dynamic disordered QWs.And the entanglement of 1st GF QWs is greater than that of the TM QWs,being followed closely by the entanglement of the second class of GF(2nd GF)QWs.For the static QWs,the entanglement of three kinds of the aperiodic QWs are also close to the maximal value and 1st GF QWs can achieve the maximum entangled state.The entanglement of the TM QWs is between1st GF QWs and 2nd GF QWs.However,the entanglement of the static disordered QWs is less than that of three kinds of the aperiodic QWs.This is different from those of the dynamic QWs.From these results,we can conclude that the dynamic and static 1st GF QWs can also be considered as maximal entanglement generators.